Method and apparatus for modeling devices having different geometries

ABSTRACT

The present invention includes a method for modeling devices having different geometries, in which a range of interest for device geometrical variations is divided into a plurality of subregions each corresponding to a subrange of device geometrical variations. The plurality of subregions include a first type of subregions and a second type of subregions. The first or second type of subregions include one or more subregions. A regional global model is generated for each of the first type of subregions and a binning model is generated for each of the second type of subregions. The regional global model for a subregion uses one set of model parameters to comprehend the subrange of device geometrical variations corresponding to the G-type subregion. The binning model for a subregion includes binning parameters to provide continuity of the model parameters when device geometry varies across two different subregions.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates generally to computer-aided electronic circuitsimulation, and more particularly, to a method of extractingsemiconductor device model parameters for use in integrated circuitsimulation.

2. Description of Related Art

While the sizes of individual devices have decreased, the complexitiesof integrated circuits have increased at a dramatic rate over the pastfew decades. As circuits have become more complex, traditionalbreadboard methods have become burdensome and overly complicated. Moderncircuit designers rely more and more on computer aids, and electroniccircuit simulators have become indispensable tools for circuit design.Examples of electronic circuit simulators include the Simulation Programwith Integrated Circuit Emphasis (SPICE) developed at the University ofCalifornia, Berkeley (UC Berkeley), and various enhanced versions orderivatives of SPICE, such as, SPICE2 or SPICE3, also developed at UCBerkeley; HSPICE, developed by Meta-software and now owned by Avant!;PSPICE, developed by Micro-Sim; and SPECTRE, developed by Cadence, ELDOdeveloped by Mentor Graphics, SSPICE developed by Silvaco, and the like.In addition, many semiconductor companies use their proprietary versionsof SPICE circuit simulators. SPICE and its various versions orderivatives will be referred to hereafter as SPICE circuit simulators.

An electronic circuit may contain a variety of circuit elements such asresistors, capacitors, inductors, mutual inductors, transmission lines,diodes, bipolar junction transistors (BJT), junction field effecttransistors (JFET), and metal-on-silicon field effect transistors(MOSFET), etc. A SPICE circuit simulator makes use of built-in orplug-in models for the circuit elements, especially semiconductor deviceelements (or device) such as diodes, BJTs, JFETs, and MOSFETs.

A model for a device mathematically represents the devicecharacteristics under various bias conditions. For example, for a MOSFETdevice model, in DC and AC analysis, the inputs of the device model arethe drain-to-source, gate-to-source, bulk-to-source voltages, and thedevice temperature. The outputs are the various terminal currents. Adevice model typically includes model equations and a set of modelparameters. The set of model parameters for a semiconductor device isoften referred as a model card (or, in abbreviation, a “model”) for thedevice. Together with the model equations, the model card directlyaffects the final outcome of the terminal currents and is used toemulate the behavior of the semiconductor device in an integratedcircuit. In order to represent actual device performance, a successfuldevice model is tied to the actual fabrication process used tomanufacture the device represented. This connection is also representedby the model card, which is dependent on the fabrication process used tomanufacture the device.

In modern device models, such as BSIM (Berkeley Short-Channel IGFETModel) and its derivatives, BSIM3, BSIM4, and BSIMPD (BerkeleyShort-Channel IGFET Model Partial Depletion), all developed at UCBerkeley, only a few of the model parameters in a model card can bedirectly measured from actual devices. The rest of the model parametersare extracted using nonlinear equations with complex extraction methods.See Daniel Foty, “MOSFET Modeling with Spice—Principles and Practice,”Prentice Hall PTR, 1997.

Since simulation algorithms and convergence techniques in circuitsimulators have become mature, the accuracy of SPICE simulation ismainly determined by the accuracy of the device models. As a result,there is a strong need for accurate device models to predict circuitperformance. Traditionally, in an integrated circuit design, onlyMOSFETs having a single drawn channel length are utilized so that asingle MOSFET model card, which is accurate for a single drawn channellength, would be sufficient. In modern integrated circuit design,however, it is not uncommon to include in an integrated circuit MOSFETshaving different geometries, i.e., different drawn channel lengths anddrawn channel widths. In addition to describing a set of devices withdifferent geometries, a device model should also satisfy criteriaoutside the device's allowed operating regime to ensure robustconvergence properties during circuit simulation. Furthermore, it isdesirable that the device model should include the effect of device sizefluctuations and technology modifications so that it can be used bycircuit designers to study the statistical behavior of the circuits, andto explore circuit design for a modified or more advanced technology.

Before scalable models were developed, binning was used to expand thesingle device model cards to comprehend a broader range of devicegeometrical variations. When modeling MOSFET devices using binning, ageometrical space constituted by ranges of interest for the channellength and width is divided into smaller regions or bins, and adifferent binning model card is created for each of these bins. Althoughthe binning model cards, when properly created, can accurately modeldevice behavior in a broad range of device sizes, it is less scalableand involves many additional parameters that have no physical meanings.Also, to obtain the binning model cards with good accuracy, test resultsfrom many differently sized devices are required. Most importantly,since each binning model is created for its own bin in isolation fromthe creation of the binning models for the other bins, binning canresult in discontinuity in device characteristics as the device geometryis varied across the boundaries of adjacent bins. This discontinuity cancomplicate statistical analysis of device and circuit behavior and causeconvergence problem during circuit simulation.

To overcome the problems of binning, scalable device models aredeveloped. A scalable device model, such as BSIM3, BSIM4, BSIMPD,includes model equations that comprehend a wide range of devicegeometrical variations and it allows the use of one set of modelparameters (or a single global model card) to model devices over therange of geometrical variations. A scalable model is generally aphysical model because many of its model equations are based on devicephysics. The global model card thus has better scalability than thebinning model cards and there is no concern about discontinuity. Themodeling accuracy, however, is sometimes not satisfactory, especiallywhen it is used to comprehend relatively large devices as well asdeep-submicron devices (e.g., devices with drawn channel length lessthan 0.1 μm or drawn channel width less than 0.13 μm), due to thecomplicated process and device physics associated with these smallergeometries.

SUMMARY OF THE INVENTION

The present invention includes a new method for modeling devices havingdifferent geometries. In one embodiment of the present invention, thegeometries of the devices to be modeled are in a geometrical spacerepresenting a range of channel lengths and channel widths, and thegeometrical space is divided into a plurality of subregions eachcorresponding to a subrange of device geometrical variations. Theplurality of subregions include a first set of subregions and a secondset of subregions. The first or second set of subregions include one ormore subregions. A regional global model is generated for each of thefirst set of subregions based on model equations and measurement datataken from a plurality of test devices. A binning model is generated foreach of the second set of subregions based on model parameters extractedfor one or more subregions in the first set of subregions. The regionalglobal model for a subregion uses one set of model parameters tocomprehend the subrange of device geometrical variations correspondingto the subregion. The binning model for a subregion includes binningparameters to provide continuity of the model parameters when devicegeometry varies across two different subregions.

The present invention also includes a computer readable mediumcomprising computer executable program instructions that when executedcause a digital processing system to perform a method for extractingsemiconductor device model parameters. The method includes the steps ofdividing a geometrical space including the different geometries into afirst set of subregions and a second set of subregions, the first or thesecond set of subregions including one or more subregions; extracting aset of model parameters for each of the first set of subregions usingmodel equations associated with the device model and measurement dataobtained from a plurality of test devices; and determining binningparameters for each of the second set of subregions using one or moremodel parameters associated with one or more subregions in the first setof subregions.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a system according to an embodiment of thepresent invention;

FIG. 2A is a flowchart illustrating a method for modeling devices withvarious geometries in accordance with an embodiment of the presentinvention;

FIG. 2B is a flowchart illustrating a method for generating regionalglobal models according to one embodiment of the present invention;

FIG. 2C is a flowchart illustrating an optimization process used in themethod for generating regional global models according to one embodimentof the present invention;

FIG. 2D is a flowchart illustrating a method for generating binningmodels according to one embodiment of the present invention;

FIG. 3A is a block diagram illustrating a top view of a typical MOSFETdevice;

FIG. 3B is a chart illustrating a device geometrical space;

FIG. 3C is a chart illustrating definition of subregions in a devicegeometrical space according to one embodiment of the present invention;

FIG. 3D is a chart illustrating definition of subregions in a devicegeometrical space according to an alternative embodiment of the presentinvention;

FIG. 4 is a block diagram of a model definition input file in accordancewith an embodiment of the present invention;

FIG. 5A is a graph illustrating test device geometries used to obtainexperimental data for extracting regional global model parameters inaccordance with an embodiment of the present invention;

FIG. 5B is a graph illustrating test device geometries used to obtainexperimental data for extracting regional global model parameters inaccordance with an alternative embodiment of the present invention;

FIG. 6 is a diagrammatic cross sectional view a of asilicon-on-insulator MOSFET device for which model parameters areextracted in accordance with an embodiment of the present invention;

FIGS. 7A-7D are examples of current-voltage (I-V) curves representingsome of the terminal current data for the test devices;

FIG. 8 is a flow chart illustrating in further detail a parameterextraction process in accordance with an embodiment of the presentinvention;

FIG. 9 is a flow chart illustrating in further detail a DC parameterextraction process in accordance with an embodiment of the presentinvention;

FIG. 10 is a flow chart illustrating a process for extracting diodecurrent related parameters in accordance with an embodiment of thepresent invention; and

FIG. 11 is a flow chart illustrating a process for extracting impactionization current related parameters in accordance with an embodimentof the present invention.

DETAILED DESCRIPTION OF THE INVENTION

As shown in FIG. 1, system 100, according to one embodiment of thepresent invention, comprises a central processing unit (CPU) 102, whichincludes a RAM, and a disk memory 110 coupled to the CPU 102 through abus 108. The system 100 further comprises a set of input/output (I/O)devices 106, such as a keypad, a mouse, and a display device, alsocoupled to the CPU 102 through the bus 108. The system 100 may furtherinclude an input port 104 for receiving data from a measurement device(not shown), as explained in more detail below. The system 100 may alsoinclude other devices 122. An example of system 100 is a Pentium 133PC/Compatible computer having RAM larger than 64 MB and a hard disklarger than 1 GB.

Memory 110 has computer readable memory spaces such as database 114 thatstores data, memory space 112 that stores operating system 112 such asWindows 95/98/NT4.0/2000, which has instructions for communicating,processing, accessing, storing and searching data, and memory space 116that stores program instructions (software) for carrying out the methodof according to one embodiment of the present invention. Memory space116 may be further subdivided as appropriate, for example to includememory portions 118 and 120 for storing modules and plug-in models,respectively, of the software.

A process 200 for modeling devices with various geometries, as shown inFIG. 2A, includes step 220 in which a device geometry space is dividedinto a plurality of subregions. A first subset of the plurality ofsubregions include one or more G-type subregions, i.e., subregions forregional global model generation, and a second subset of the pluralityof subregions include one or more B-type subregions, i.e., subregionsfor binning model generation. Process 200 further includes step 230 inwhich a regional global model is generated for each of the G-typesubregions and step 240 in which a binning model is generated for eachof the B-type subregions.

To illustrate the device geometry, a illustrative layout of a MOSFETdevice is shown in FIG. 3A. Referring to FIG. 3A, the MOSFET device 301includes a gate 305, and source/drain diffusion regions 302 on two sidesof the gate 305 in an active region 303. Active region 303 may bebordered on some or all sides by isolation (or field) regions 306, whichseparate MOSFET 301 from other devices in an IC. The extent of gate 305as drawn in the layout along the y-direction shown in FIG. 3A is calledthe drawn channel length (or channel length) L of the MOSFET device 301,while the extent of source/drain diffusion regions 302 as drawn in thelayout along the z direction is called the drawn channel width (orchannel width) W of the MOSFET device 301.

A device geometrical space can be used to represent a range of interestfor the MOSFET device geometrical variations. FIG. 3B illustrates ageometrical space 300 corresponding to channel length variations rangingfrom L_(min) to L_(max) and channel width variations ranging fromW_(min) to W_(max). FIG. 3C illustrates an example of dividing thedevice geometrical space 300 in step 220 of process 200. As shown inFIG. 3C, the geometrical space 300 for a MOSFET device is divided into apluality of subregions such as subregions 310, 320, and 330, among whichsubregions 310 and 330 are G-type subregions, and subregion 320 is aB-type subregion. The G-type subregions 310 and 330 are separated by theB-type subregion 320. As shown in FIG. 3C, the range of channel widthvariations in the geometrical space 300 spans from W_(min) to W_(max),and subregion 310 covers a drawn channel width subrange of W₁=W_(min) toW₂, subregion 320 covers a drawn channel width subrange of W₂ to W₃, andsubregion 330 covers a drawn channel width subrange of W₃ to W₄=W_(max).In the example shown in FIG. 3C, the divisions of the subregions aremade along the drawn channel length axis so that each subregionemcompass all of the channel length variations in the geometrical space300 and a subrange of the channel width variations. The subregions aredivided in the way because many MOSFET device models scale better forchannel length variations than for channel width variations. FIG. 3C,however, only shows one way of dividing the geometrical space 300.Different ways of dividing the geometry space can be used for differentapplications without departing from the scope of the present invention.

For example, FIG. 3D illustrates another example of dividing thegeometrical space 300 according to an alternative embodiment of thepresent invention. As shown in FIG. 3D, the geometrical space 300 isdivided into nine subregions including four G-type subregion 342, 344,346, and 348, and five B-type subregions 351, 353, 355, 357, and 359.Subregion 342 covers a drawn channel width subrange of W₁=W_(min) to W₂and a drawn channel length subrange of L₁=L_(min) to L₂, subregion 344covers a drawn channel width subrange of W₁ to W₂ and a drawn channellength subrange of L₃ to L₄=L_(max), subregion 346 covers a drawnchannel width subrange of W₃ to W₄=W_(max) and a drawn channel lengthsubrange of L₁ to L₂, and subregion 348 covers a drawn channel widthsubrange of W₃ to W₄ and a drawn channel length subrange of L₃ to L₄.Also subregion 351 covers a drawn channel width subrange of W₁ to W₂ anda drawn channel length subrange of L₂ to L₃, subregion 353 covers adrawn channel width subrange of W₂ to W₃ and a drawn channel lengthsubrange of L₁ to L₂, subregion 355 covers a drawn channel widthsubrange of W₂ to W₃ and a drawn channel length subrange of L₂ to L₃,subregion 357 covers a drawn channel width subrange of W₂ to W₃ and adrawn channel length subrange of L₃ to L₄, and subregion 359 covers adrawn channel width subrange of W₃ to W₄ and a drawn channel lengthsubrange of L₂ to L₃.

FIG. 2B illustrates in further detail the regional global modelgeneration step 230 in process 200. As shown in FIG. 2B, step 230includes substep 232, in which the device model for modeling the devicesis selected. When system 100 is used to carry out process 200, the modelmay be stored in the database 114 as a model definition file, andsubstep 232 includes loading the model definition file from database114. The model definition file provides information associated with thedevice model. Referring to FIG. 4, the model definition file 400comprises a general model information field 410, a parameter definitionfield 420, and an operation point definition field 430. The generalmodel information field 410 includes general information about thedevice model, such as model name, model version, compatible circuitsimulators, model type and binning information. The parameter definitionfield 420 defines the parameters in the model. For each parameter, themodel definition file specifies information associated with theparameter, such as parameter name, default value, parameter unit, datatype, and optimization information. The operation point definitionsection 430 defines operation point or output variables, such as deviceterminal currents, threshold voltage, etc., used by the model. In oneembodiment of the present invention, the selected model is a scalableMOSFET device model such as BSIM3, BSIM4, BSIMPD, etc.

The regional global model generation step 230 further includes substep234 in which a G-type subregion is selected, and substep 236 in whichregional global model parameters associated with the G-type subregionare extracted so that a regional global model is generated for thesubregion Afterwards, if it is determined in substep 238 that moreG-type subregions are available for regional global model generation,another G-type subregion is selected and a regional global model isgenerated for that subregion. This process continues until a regionalglobal model is generated for each of the G-type subregions.

During the extraction substep 236, model equations associated with theselected device model and measurement data from a plurality of testdevices are used to extract the model parameters associated with aselected subregion. The measurement data include physical measurementsfrom a set of test devices. In one embodiment of the present invention,the measurement data include terminal current data and capacitance datameasured from test devices under various bias conditions, and can beobtained using a conventional semiconductor device measurement tool thatis coupled to system 100 through input port 104. The measurement dataare then organized by CPU 102 and stored in database 114. The testdevices are typically manufactured using the same or similar processtechnologies for fabricating the devices to be modeled. In oneembodiment of the present invention, a set of test devices being of thesame type as the devices to be modeled are used for the measurement. Therequirement for the geometries of the test devices can vary depending ondifferent applications. Ideally, as shown in FIG. 5A, the set of devicesfor a selected subregion, such as subregion 330, include:

-   -   a. one largest device, meaning the device with the longest drawn        channel length and widest drawn channel width, as represented by        dot 502;    -   b. one smallest device, meaning the device with the shortest        drawn channel length and smallest drawn channel width, as        represented by dot 516;    -   c. one device with the smallest drawn channel width and longest        drawn channel length, as represented by dot 510;    -   d. one device with the widest drawn channel width and shortest        drawn channel length, as represented by dot 520;    -   e. three devices having the widest drawn channel width and        different drawn channel lengths in the selected subregion, as        represented by dots 504, 506, and 508;    -   f. two devices with the shortest drawn channel length and        different drawn channel widths in the selected subregion, as        represented by dots 512 and 514;    -   g. two devices with the longest drawn channel length and        different drawn channel widths in the selected subregion, as        represented by dots 522 and 524;    -   h. (optionally) up to three devices with smallest drawn channel        width and different drawn channel lengths in the selected        subregion, as represented by dots 532, 534, and 536; and    -   i. (optionally) up to three devices with medium drawn channel        width (about halfway between the widest and smallest drawn        channel width) and different drawn channel lengths in the        selected subregion, as represented by dots 538, 540, and 542.

If in practice, it is difficult to obtain measurements for all of theabove required devices sizes, a smaller set of different sized devicescan be used. For example, the different device sizes shown in FIG. 5Bare sufficient for extracting model parameters for subregion 330,according to one embodiment of the present invention. The test devicesas shown in FIG. 5B include:

-   -   a. one largest device, meaning the device with the longest drawn        channel length and widest drawn channel width, as represented by        dot 502;    -   b. one smallest device, meaning the device with the shortest        drawn channel length and smallest drawn channel width, as        represented by dot 516;    -   c. (optional) one device with the smallest drawn channel width        and longest drawn channel length, as represented by dot 510;    -   d. one device with the widest drawn channel width and shortest        drawn channel length, as represented by dot 520;    -   e. one device and two optional devices having the widest drawn        channel width and different drawn channel lengths in the        selected subregion, as represented by dots 504, 506, and 508,        respectively;    -   f. (optional) two devices with the shortest drawn channel length        and different drawn channel widths in the selected subregion, as        represented by dots 512 and 514.

For a given device model, there are usually different ways to extractthe model parameters. Also, depending on the type of devices to bemodeled, the specific device model used to model the devices, or thespecific method of extracting the model parameters associated with thedevice model, different measurement data may need to be taken from testdevices. As an example, when the devices to be modeled are MOSFETdevices and version 2 of the BSIM3 model is used for the modeling, thetypes of data to be measured and the model parameter extraction methoddescribed by Yuhua Cheng and Chenming Hu in “MOSFET Modeling & BSIM3User's Guide,” Kluwer Academic Publishers, 1999, which is incorporatedherein by reference in its entirety, can be used to generate theregional global models. As another example, when the BSIM4 model is usedto model the MOSFET devices, the types of data to be measured and themodel parameter extraction method described in Provisional PatentApplication No. 60/407,251 filed on Aug. 30, 2002, which is incorporatedherein by reference in its entirety, can be used to generate theregional global models. As yet another example, when the devices to bemodeled are silicon-on-insulator(SOI) MOSFET devices and the BSIMPDmodel is used, the types of data to be measured and the model parameterextraction method described below and also in Provisional PatentApplication Ser. No. 60/368,599 filed on Mar. 29, 2002, which isincorporated herein by reference in its entirety, can be used togenerate regional global models. Some aspects of the model parameterextraction methods for the BSIM4 and BSIMPD models are described in the“BSIMPro+User Manual—Device Modeling Guide,” by Celestry Design Company,2001, which is also incorporatated herein by reference in its entirety.

Although the embodiments of the present invention can be applied to manydifferent methods for extracting model parameters for many differenttypes of devices, the parameter extraction process for a SOI MOSFETdevice is described below to aid in the understanding of one embodimentof the present invention. The present invention, however, is not limitedto the type of devices to be modeled, the specific device model used tomodel the devices, or the specific method used to extract the associatedmodel parameters. As shown in FIG. 6, a SOI MOSFET device 600 maycomprise a thin silicon on oxide (SOI) film 680, having a thicknessT_(si), on top of a layer of buried oxide 660, having a thicknessT_(box). The SOI film 680 has two doped regions, a source 630 and adrain 650, separated by a body region 640. The SOI MOSFET also comprisesa gate 610 on top of the body region 640 and is separated from SOI film680 by a thin layer of gate oxide 620. The SOI MOSFET 600 is formed on asemiconductor substrate 670.

The SOI MOSFET as described can be considered a five terminal (node)device. The five terminals are the gate terminal (node g), the sourceterminal (node s), the drain terminal (node d), the body terminal (nodep), and the substrate terminal (node e). Nodes g, s, d, and e can beconnected to different voltage sources while node p can be connected toa voltage source or left floating. In the floating body configurationthere are four external biases, the gate voltage (V_(g)), the drainvoltage (V_(d)), the source voltage (V_(s)) and the substrate biasV_(e). If body contact is applied, there will be an additional externalbias, the body contact voltage (V_(p)).

For ease of further discussion, Table I below lists the symbolscorresponding to the physical variables associated with the operation ofSOI MOSFET device 600.

TABLE I C_(pd) body to drain capacitance C_(ps) body to sourcecapacitance I_(c) parasitic bipolar transistor collector current I_(p)current through body (p) node I_(bjt) parasitic bipolar junctiontransistor current I_(d) current through drain (d) node I_(dgidl) gateinduced leakage current at the drain I_(diode) diode current I_(ds)current flowing from source to drain I_(dsat) drain saturation currentI_(c) current through substrate (e) node I_(g) (or J_(gh)) gate oxidetunneling current I_(gs) current flowing from source to gate I_(ii)impact ionization current I_(s) current through source (s) nodeI_(sgidl) gate induced drain leakage current at the source L_(drawn)drawn channel length L_(eff) effective channel length R_(d) drainresistance R_(s) source resistance R_(ds) drain/source resistanceR_(out) output resistance V_(b) internal body voltage V_(bs) voltagebetween node p and node s V_(d) drain voltage V_(DD) maximum operatingDC voltage V_(ds) voltage between node d and node s V_(e) substratevoltage V_(g) gate voltage V_(gs) voltage between node g and node sV_(p) body contact voltage V_(s) source voltage V_(th) threshold voltageW_(drawn) drawn channel width W_(eff) effective channel width

In order to model the behavior of the SOI MOSFET device 600 using theBSIMPD model, experimental data are used to extract model parametersassociated with the model. In one embodiment of the present invention,for each test device, terminal currents are measured under differentterminal bias conditions. These terminal current data are put togetheras I-V curves representing the I-V characteristics of the test device.In one embodiment of the present invention, as listed in FIG. 6, foreach test device, the following I-V curves are obtained:

-   -   a. Linear region I_(d) vs. V_(gs) curves for a set of V_(p)        values. These curves are obtained by grounding the s node and e        node, setting V_(d) to a low value, such as 0.05V, and for each        of the set of V_(p) values, measuring I_(d) while sweeping V_(g)        in step values across a range such as from 0 to V_(DD).    -   b. Saturation region I_(d) vs. V_(gs) curves for a set of V_(p)        values. These curves are obtained by grounding the s node and e        node, setting V_(d) to a high value, such as V_(DD), and for        each of the set of V_(p) values, measuring I_(d) while sweeping        V_(g) in step values across a range such as from 0 to V_(DD).    -   c. I_(d) vs. V_(gs) curves for different V_(d), V_(p) and V_(e)        values, obtained by grounding s node, and for each combination        of V_(d), V_(p) and V_(e) values, measuring I_(d) while sweeping        V_(g) in step values across a range such as from −V_(DD) to        V_(DD).    -   d. I_(g) vs. V_(gs) curves for different V_(d), V_(p) and V_(e)        values, obtained by grounding s node, and for each combination        of V_(d) V_(p) and V_(e) values, measuring I_(g) while sweeping        V_(g) in step values across a range such as from −V_(DD) to        V_(DD).    -   e. I_(s) vs. V_(ds) curves for different V_(g), V_(p) and V_(e)        values, obtained by grounding s node, and for each combination        of V_(g), V_(p) and V_(e) values, measuring I_(s) while sweeping        V_(d) in step values across a range such as from 0 to V_(DD).    -   f. I_(p) vs. V_(gs) curves for different V_(d), V_(p) and V_(e)        values, obtained by grounding s node, and for each combination        of V_(d), V_(p) and V_(e) values, measuring I_(p) while sweeping        V_(g) in step values across a range such as from −V_(DD) to        V_(DD).    -   g. I_(d) vs. V_(gs) curves for different V_(d), V_(p) and V_(e)        values, obtained by grounding s node, and for each combination        of V_(p), V_(d) and V_(e) values, measuring I_(d) while sweeping        V_(g) in step values across a range such as from −V_(DD) to        V_(DD).    -   h. I_(d) vs. V_(ps) curves for different V_(d), V_(g) and V_(e)        values, obtained by grounding s node, and for each combination        of V_(g), V_(d) and V_(e) values, measuring I_(d) while sweeping        V_(p) in step values across a range such as from −V_(DD) to        V_(DD).    -   i. Floating body I_(d) vs. V_(gs) curves for different V_(d) and        V_(e) values, obtained by grounding s node, floating b node, and        for each combination of V_(d) and V_(e) values, measuring I_(d)        while sweeping V_(g) in step values across a range such as from        0 to V_(DD).    -   j. Floating body I_(d) vs. V_(ds) curves for different V_(g) and        V_(e) values, obtained by grounding s node, floating b node, and        for each combination of V_(d) and V_(e) values, measuring I_(d)        while sweeping V_(g) in step values across a range such as from        0 to V_(DD).

As examples, FIG. 7A shows a set of linear region I_(d) vs. V_(gs)curves for different V_(ps) values, FIG. 7B shows a set of saturationregion I_(d) vs. V_(gs) curves for different V_(ps) values, FIG. 7Cshows a set of I_(d) vs. V_(ds) curves for different V_(gs) values whileV_(ps)=0.5V and V_(es)=0; FIG. 7D shows a set of I_(d) vs. V_(ds) curvesfor different V_(gs) values while V_(ps)=0.25V and V_(es)=0.

In addition to the terminal current data, for each test device,capacitance data are also collected from the test devices under variousbias conditions. The capacitance data can be put together intocapacitance-current (C-V) curves. In one embodiment of the presentinvention, the following C-V curves are obtained:

-   -   a. C_(ps) vs. V_(ps) curve obtained by grounding s node, setting        I_(e) and I_(d) to zero, or to very small values, and measuring        C_(ps) while sweeping V_(p) in step values across a range such        as from −V_(DD) to V_(DD).    -   b. C_(pd) vs. V_(ps) curve obtained by grounding s node, setting        I_(e) and I_(s) to zero, or to very small values, and measuring        C_(pd) while sweeping V_(p) in step values across a range such        as from −V_(DD) to V_(DD).

A list of the model parameters in the BSIMPD model are provided inAppendix A. The BSIMPD model is described in more detail in the“BSIM4.0.0 MOSFET Model—User's Manual,” by Liu, et al., Department ofElectrical Engineering and Computer Sciences, University of California,Berkeley, 2000, which is incorporated herein by reference. As shown inFIG. 8, in one embodiment of the present invention, the parameterextraction step 230 comprises extracting base parameters 810; extractingother DC model parameters 820; extracting temperature dependent relatedparameters 830; and extracting AC parameters 840. In base parametersextraction step 810, base parameters, such as V_(th) (the thresholdvoltage at V_(bs)=0), K₁ (the first order body effect coefficient), andK₂ (the second order body effect coefficient) are extracted based onprocess parameters corresponding to the process technology used tofabricate the SOI MOSFET device to be modeled. The base parameters arethen used to extract other DC model parameters at step 820, which isexplained in more detail in connection with FIGS. 9, 10, and 11 below.

The temperature dependent parameters are parameters that may vary withthe temperature of the device and include parameters such as: Ktl1(temperature coefficient for threshold voltage); Ua1 (temperaturecoefficient for U_(a)), and Ub1 (temperature coefficient for U_(b)),etc. These parameters can be extracted using a conventional parameterextraction method.

The AC parameters are parameters associated with the AC characteristicsof the SOI MOSFET device and include parameters such as: CLC (constantterm for the short chanel model) and moin (the coefficient for thegate-bias dependent surface potential), etc. These parameters can alsobe extracted using a conventional parameter extraction method.

As shown in FIG. 9, the DC parameter extraction step 820 furthercomprises: extracting I_(diode) related parameters (step 902);extracting I_(bjt) related parameters (step 904); extracting V_(th)related parameters (step 906); extracting I_(dgid1) and I_(sgid1)related parameters (step 908); extracting I_(g) (or J_(gb)) relatedparameters (step 910); extracting L_(eff) related parameters, R_(d)related parameters, and R_(s) related parameters (step 912); extractingmobility related parameters and W_(eff) related parameters (step 914);extracting V_(th) geometry related parameters (step 916); extractingsub-threshold region related parameters (step 918); extractingparameters related to drain-induced barrier lower than regular (DIBL)(step 920); extracting I_(dsat) related parameters (step 922);extracting I_(ii) related parameters (step 924); and extracting junctionparameters (step 926).

The equation numbers below refer to the equations set forth in AppendixB.

In step 902, parameters related to the calculation of the diode currentI_(diode) are extracted. These parameters include, J_(sbjt), n_(dio),R_(body), n_(recf) and j_(srec). As shown in more detail in FIG. 10,step 902 comprises: extracting J_(sbjt) and n_(dio) (step 1010);extracting R_(body) (step 1020); and extracting n_(recf) and j_(srec)(step 1030).

Model parameters J_(sbjt) and n_(dio) are extracted in step 1010 fromthe recombination current in neutral body equations (Equations14.5a-14.5.f) using measured data in the middle part of the I_(d) vsV_(ps) curves taken from the largest test device (test device havinglongest L_(drawn)and widest W_(drawn)). By using the largest device,α_(bjt)→0. Then, assuming A_(hli)=0, E_(hlid) will also equal zero.Therefore Equations 14.5.d-14.5.f can be eliminated. The set ofequations is thus reduced to two equations (14.5.b and 14.5.c) with twounknowns, resulting in quick solution for J_(sbjt) and n_(dio). In oneembodiment of the present invention, the middle part of an I_(d) vsV_(ps) curve corresponds to the part of the I_(d) vs V_(ps) curve withV_(ps) ranging from about 0.3V to about 0.8V. In another embodiment, themiddle part of the I_(d) vs V_(ps) curve corresponds to V_(ps) rangingfrom about 0.4V to about 0.7V.

R_(body) is extracted in step 1020 from the body contact currentequation (Equations 13.1-13.3) using measured data in the high currentpart of the I_(d) vs I_(ps) curves. In one embodiment of the presentinvention, the high current part of an I_(d) vs V_(ps) curve correspondsto the part of the I_(d) vs V_(ps) curve with V_(ps) ranging from about0.8V to about 1V.

The first order parameters, n_(recf) and j_(srec) are extracted in step1030 from the recombination/trap-assist tunneling current in depletionregion equations (Equations 14.3.a and 14.3.b), also using the I_(d) vsI_(ps) curves taken from one shortest device. The remaining I_(diode)related parameters are second order parameters and may be neglected.

Referring back to FIG. 9, the parasitic lateral bipolar junctiontransistor current (I_(bjt)) related parameter L_(n) is extracted instep 904. In this step, a set of I_(c)/I_(p) vs. V_(ps) curves areconstructed from the I_(d) vs. V_(ps) curves taken from one shortestdevice. Then the bipolar transport factor equations (Equation 14.1)wherein I_(c)/I_(b)=α_(bjt)/1−α_(bjt) are used to extract L_(n).

In step 906, threshold voltage V_(th) related parameters, such asV_(th0), k1, k2, and Nch, are extracted by using the linear I_(d) vsV_(g) curves measured from the largest device.

In step 908, parameters related to the gate induced drain leakagecurrent at the drain and at the source (I_(dgid1)) and the gate induceddrain leakage current at the source (I_(sgid1), ) are extracted. TheI_(dgid1) and I_(sgid1) related parameters include parameters such asα_(gid1) and β_(gid1), and are extracted using the I_(d) vs. V_(g)curves and Equations 12.1 and 12.2.

In step 910 the oxide tunneling current (I_(g), also designated asJ_(gb)) related parameters are extracted. The I_(g) related parametersinclude parameters such as V_(EvB), α_(gb1), β_(gb1), V_(gb1), V_(ECB),α_(gb2), β_(gb2), and V_(gb2), and are extracted using the I_(g) vs.V_(g) curves and equations 17.1a-f and 17.2 a-f.

In step 912, parameters related to the effective channel length L_(eff),the drain resistance R_(d) and source resistance R_(s) are extracted.The L_(eff), R_(d) and R_(s) related parameters include parameters suchas L_(int), and R_(dsw) and are extracted using data from the linearI_(d) vs V_(g) curves as well as the extracted V_(th) related parametersfrom step 906.

In step 914, parameters related to the mobility and effective channelwidth W_(eff), such as μ₀, U_(a), U_(b), U_(c), Wint, Wri, Prwb, Wr,Prwg, R_(dsw), Dwg, and Dwb, are extracted, using the linear I_(d) vsV_(g) curves, the extracted V_(th), and L_(eff), R_(d) and R_(s) relatedparameters from steps 906 and 912.

Steps 906, 912, and 914 can be performed using a conventional BSIMPDmodel parameter extraction method. Discussions about some of theparameters involved in these steps can be found in: “A new method todetermine effective MOSFET channel length,” by Terada K. and Muta H,Japan J Appl. Phys. 1979:18:953-9; “A new Method to determine MOSFETchannel length,” by Chem J., Chang P., Motta R., and Godinho N., IEEETrans Electron Dev 1980: ED-27:1846-8; and “Drain and source resistancesof

short-channel LDD MOSFETs,” by Hassan Md Rofigul, et al., Solid-StateElectron 1997:41:778-80; which are incorporated by reference herein.

In step 916, the threshold voltage V_(th) geometry related parameters,such as D_(VT0), D_(VT1), D_(VT2), N_(LX1), D_(VT0W), D_(VT1W),D_(VT2W), k₃, and k_(3b), are extracted, using the linear I_(d) vs V_(g)curve, the extracted V_(th), L_(eff), and mobility and W_(eff) relatedparameters from steps 906, 912, and 914, and Equations 3.1 to 3.10.

In step 918, sub-threshold region related parameters, such as C_(it),Nfactor, V_(off), D_(dsc), and C_(dscd), are extracted, using the linearI_(d) vs V_(gs) curves, the extracted V_(th), L_(eff) and R_(d) andR_(s) and mobility and W_(eff) related parameters from steps 906, 912,and 914, and Equations 5.1 and 5.2.

In step 920, DIBL related parameters, such as D_(sub), Eta0 and Etab,are extracted, using the saturation I_(d) vs V_(gs) curves and theextracted V_(th) related parameters from step 906, and Equations 3.1 to3.10.

In step 922, the drain saturation current I_(dsat) related parameters,such as B0, B1, A0, Keta, and A_(gs), are extracted using the saturationI_(d) vs V_(d) curves, the extracted V_(th), L_(eff) and R_(d) andR_(s), mobility and W_(eff), V_(th) geometry, sub-threshold region, andDIBL related parameters from steps 906, 912, 914, 916, and 918, andEquations 9.1 to 9.10.

In step 924, the impact ionization current I_(ii) related parameters,such as α₀, β₀, β₁, β₂, V_(dsatii), and L_(ii), are extracted, asdiscussed in detail in relation to FIG. 11 below.

FIG. 11 is a flow chart illustrating in further detail the extraction ofthe impact ionization current I_(ii) related parameters (step 924). Inone embodiment of the present invention, data from the I_(p) v V_(gs)and I_(d) v V_(gs) curves measured from one or more shortest devices areused to construct the I_(ii)/I_(d) vs V_(ds) curves for the one or moreshortest devices (step 1110). This begins by identifying the point whereV_(gs) is equal to V_(th) for each I_(p) v V_(gs) curve. This point isfound by setting V_(gst)=0. When V_(gst)=0, V_(gsstep)=0. Then, usingthe impact ionization current equation, Equation 11.1, the I_(ii)/I_(d)vs V_(ds) curve can be obtained.

After the I_(ii)/I_(d) vs V_(ds) curve is obtained, L_(ii) is set equalto zero and V_(dsatti0) is set to 0.8 (the default value). Using theI_(ii)/I_(d) vs V_(ds) curve β₁, α₀, β₂, β₀ are extracted 1115 from theimpact ionization current equation for I_(ii), Equation 11.1.

In 1120, V_(dsatii) is interpolated from a constructed I_(ii)/I_(d) vsV_(ds) curve by identifying the point at which I_(p)/I_(d)=α₀.

Following the interpolation, using a conventional optimizer such as theNewton-Raphson algorithm, β₁, β₂, β₀ are optimized 1125.

Step 1120 is repeated for each constructed I_(ii)/I_(d) vs V_(ds) curve.This results in an array of values for V_(dsatii). Using these valuesfor V_(dsatii), L_(ii) is extracted 1135 from the V_(dsatii) equationfor the impact ionization current (Equation 11.3).

The extracted β₁, α₀, β₂, β₀, L_(ii), and V_(dsatti0) are optimized atstep 1140 by comparing calculated and measured I_(ii)/I_(d) vs V_(ds)curves for the one or more shorted devices.

The next step, 1145 uses the extracted parameters from the I_(ii) andV_(dsatii) equations to calculate V_(gsstep) using Equation 11.4 for thelargest device. Then 1150, using a local optimizer such as the NewtonRaphson algorithm, and the V_(gsstep) equation, Equation 11.4, S_(ii1),S_(ii2), S_(ii0) are determined.

In the next step 1155 the last of the I_(ii) related parameters isextracted using the shortest device. In this step, E_(satii) is solvedfor by using the V_(gsstep) equation, Equation 11.4, and theI_(ii)/I_(d) vs V_(ds) curve. The extraction of the I_(ii), relatedparameters is complete.

Referring back to FIG. 9, in step 926, the junction parameters, such asCjswg, Pbswg, and Mjswg, are extracted using the C_(ps) vs. V_(ps) andC_(pd) vs. V_(ps) curves, and Equations 21.4.b.1 and 21.4.b.2.

In performing the DC parameter extraction steps (steps 901-926), it ispreferred that after the I_(diode) and I_(bjt) related parameters areextracted in steps 902 and 904, I_(diode) and I_(bjt) are calculatedbased on these parameters and the model equations. This calculation isdone for the bias condition of each data point in the measured I-Vcurves. The I-V curves are then modified for the first time based on thecalculated I_(diode) and I_(bjt) values. In one embodiment of thepresent invention, the I-V curves are first modified by subtracting thecalculated I_(diode) and I_(bjt) values from respective I_(s), I_(d),and I_(p) data values. For example, for a test device having drawnchannel length L_(T) and drawn channel width W_(T), if under biascondition where V_(s)=V_(s) ^(T), V_(d)=V_(d) ^(T), V_(p)=V_(p) ^(T),V_(e)=V_(e) ^(T), and V_(g)=V_(g) ^(T), the measured drain current isI_(d) ^(T), then after the first modification, the drain current will beI_(d) ^(first-modifies)=I_(d) ^(T)-I_(diode) ^(T)-I_(bjt) ^(T), whereI_(diode) ^(T) and I_(bjt) ^(T) are calculated I_(diode) and I_(bjt)values, respectively, for the same test device under the same biascondition. The first-modified I-V curves are then used for additional DCparameter extraction. This results in higher degree of accuracy in theextracted parameters. In one embodiment the I_(diode) and I_(bjt)related parameters are extracted before extracting other DC parameters,so that I-V curve modification may be done for more accurate parameterextraction. However, if such accuracy is not required, one can choosenot to do the above modification and the I_(diode) and I_(bjt) relatedparameters can be extracted at any point in the DC parameter extractionstep 820.

Similalry, after the I_(dgid1), I_(sgid1) and I_(g) related parametersare extracted in steps 908 and 910, I_(dgid1), I_(sgid1) and I_(g) arecalculated based on these parameters and the model equations. Thiscalculation is done for the bias condition of each data point in themeasured I-V curves. The I-V curves or the first-modified I-V curves arethen modified or further modified based on the calculated I_(dgid1),I_(sgid1) and I_(g) values. In one embodiment of the present invention,the I-V curves or modified I-V curves are modified or further modifiedby subtracting the calculated I_(dgid1), I_(sgid1) and I_(g) values fromrespective measured or first-modified I_(s), I_(d), and I_(p) datavalues. For example, for a test device having drawn channel length L_(T)and drawn channel width W_(T), if under bias condition where V_(s)=V_(s)^(T), V_(d)=V_(d) ^(T), V_(p)=V_(p) ^(T), V_(e)=V_(e) ^(T), andV_(g)=V_(g) ^(T), the measured drain current is I_(d) ^(T), then afterthe above modification or further modification, the drain current willbe I_(d) ^(modified)=I_(d) ^(T)-I_(dgid1)-I_(sgid1)-I_(g), or I_(d)^(further-modified)=I_(d) ^(first-modified)-I_(dgid1)-I_(sgid1)-I_(g),where I_(dgid1), I_(sgid1) and I_(g) are calculated I_(dgid1), I_(sgid1)and I_(g) values, respectively, for the same test device under the samebias condition. The modified or further modified I-V curves are thenused for additional DC parameter extraction. This results in higherdegree of accuracy in the extracted parameters. In one embodiment theI_(dgid1), I_(sgid1) and I_(g) related parameters are extracted beforeextracting other DC parameters that can be affected by themodifications, so that I-V curve modification may be done for moreaccurate parameter extraction. However, if such accuracy is notrequired, one can choose not to do the above modification and theI_(dgid1), I_(sgid1) and I_(g) related parameters can be extracted atany point in the DC parameter extraction step 820.

A method for extracting model parameters for a scalable device model,such as the ones stated above, usually involves an optimization processin which the differences between calculated and measured values of a setof physical quantities are minimized by adjusting the values of themodel parameters. The set of physical quantities include terminalcurrent and/or capacitance values of the devices under various biasconditions, including some of the bias conditions used to obtainmeasurement data from test devices An exemplary optimization process 260is illustrated in FIG. 2C, which combines a Newton-Raphson iterationmethod and a linear-least-square fitting routine. Referring to FIG. 2C,optimization process 260 includes step 261 in which a plurality of modelparameters are selected for optimization, and step 262 in which one ormore physical quantities are selected from the set of physicalquantities for optimization. Optimization process 260 further includesstep 263 in which a plurality of test devices are selected from the testdevices associated with the selected subregion, as discussed above inconnection with FIGS. 5A and 5B. Optimization process 260 furtherincludes step 264 in which initial values of the plurality of modelparameters are determined. For example, model parameters extracted for aprior fabrication technology or default values of the model parametersprovided by the device model can be used as the initial values of themodel parameters. Using the model equations and the initial values ofthe model parameters, optimization process 260 then proceeds tocalculate in step 265 the values of the selected of physicalquantitie(s) associated with each of the selected test device.Optimization process 260 further includes step 266 in which thecalculated values of the physical quantitie(s) associated with each ofthe selected test device are compared with corresponding measurementdata from the selected test devices using a linear least square fitroutine. With the least square fit routine, at least some of theselected plurality of model parameters are optimized by minimizing afitting error, such as error ε in the following equation:

${ɛ = {\sum\limits_{i = 1}^{N}\;( \frac{T_{mea}^{i} - T_{cal}^{i}}{T_{cal}^{i}} )^{2}}},$where T^(i) _(mea) is the measured value of a physical quantity for thei^(th) test device, T^(i) _(cal) is the calculated value of the physicalquantity for the i^(th) test device, and summation runs through theselected test devices. Step 266 determines an increment value for eachof the model parameters being optimized. Optimization process 260 thendetermines at step 268 whether the increment values for the modelparameters meet predetermined criteria, e.g., whether the incrementvalue for a parameter is small enough. If it is, the initial guess ofthe value of the parameter is the final extracted parameter value. Ifthe increment is not small enough, the initial guess of the modelparameter is adjusted by adding to it the increment value for the modelparameter, and the optimization process returns to step 264 andcontinues until the criteria are met.

When generating a regional global model for a G-type subregion, localoptimization instead of global optimization should be used. During thelocal optimization, the model parameters are extracted by fittingcurrent or capacitance values calculated form model equations tocorresponding measurement data taken from devices having geometrieswithin or on the borders of the G-type subregion. Thus, the measurementdata used in the linear least square fit routine in step 266 onlyincludes measurement data taken from test devices within or on theborders of the G-type subregion

After the regional global models are generated, as shown in FIG. 2A,process 200 in one embodiment of the present invention proceeds to step240 in which a binning model for each of the B-type subregions isgenerated. FIG. 2D illustrates a binning method 270 used in step 240 togenerate a binning model card for a B-type subregion. As shown in FIG.2D, the binning method 270 includes step 272 in which a model parameteris selected among a plurality of model parameters that can be binned.Examples of binnable model parameters for the BSIMPD model include Vth0,U0, A0, etc. Binning method 270 further includes step 274 in which oneor more boundary values of the selected model parameter is determinedusing one or more regional global model cards associated with one ormore G-type subregions adjacent the B-type subregion. In the exampleshown in FIG. 3C, when generating a binning model for the B-typesubregion 320, the boundary values of a binnable parameter P are thevalues of the parameter P in the G-type subregions 310 and 330. In theexample shown in FIG. 3D, the boundary values of P for the B-typesubregion 351 are the values of P in the G-type subregions 342 and 344,the boundary values of P for the B-type subregion 353 are the values ofP in the G-type subregions 344 and 346, the boundary values of P for theB-type subregion 355 are the values of P in the G-type subregions 342,344, 346 and 348, the boundary values of P for the B-type subregion 357are the values of P in the G-type subregions 344 and 348, and theboundary values of P for the B-type subregion 359 are the values of P inthe G-type subregions 346 and 348.

Binning method 270 further includes step 276 in which one or morebinning model parameters associated with the selected model parameterare determined. In one embodiment of the present invention, the selectedmodel parameter is written as a function of device geometry instances inthe B-type subregion. The function includes the one or more binningparameters as coefficients in the function. The binning parameters arethen determined by solving one or more equations, which are obtained byequating the selected model parameter to the one or more boundary valuesat the boundaries of the B-type subregion.

For example, when the device geometrical space 300 is divided intoG-type subregions 310 and 330, and B-type subregion 320, as shown inFIG. 3C, a model parameter P in the B-type subregion 320 can be writtenas:

$P = {P_{0} + \frac{P_{W}}{W}}$where P₀ and P_(W) are binning parameters associated with modelparameter P, and W stands for the drawn channel width. Suppose that thevalue of the model parameter P in the regional global model for theG-type subregion 310 is P′ and the value of the model parameter P in theregional global model for the G-type subregion 330 is P″, binningparameters P₀ and P_(W) can be determined by solving the followingequations:

${{P_{0} + \frac{P_{W}}{W_{2}}} = P^{\prime}},{{{{and}\mspace{14mu} P_{0}} + \frac{P_{W}}{W_{3}}} = P^{''}},$so that

${P_{0} = \frac{{W_{2}P^{''}} - {W_{3}P^{\prime}}}{W_{2} - W_{3}}},{{{and}\mspace{14mu} P_{W}} = {W_{2}W_{3}{\frac{P^{''} - P^{\prime}}{W_{2} - W_{3}}.}}}$This way, the parameter P is continuous when device width is variedacross the boundary between G-type region 310 and B-type region 320 andacross the boundary between B-type region 320 and P-type region 330.

Alternatively, when the device geometrical space 300 is divided as shownin FIG. 3D, a model parameter P in the B-type subregion 355 can bewritten as:

$P = {P_{0} + \frac{P_{W}}{W} + \frac{P_{L}}{L} + \frac{P_{P}}{W \times L}}$where P₀, P_(W), P_(L), and P_(P) are binning parameters associated withmodel parameter P, W stands for the drawn channel width and L stands forthe drawn channel length. Suppose that the values of the model parameterP in the regional global models for the G-type subregions 342, 344, 246,and 348 are P₁, P₂, P₃, and P₄, respectively, binning parameters P₀P_(W), P_(L), and P_(P) can be determined by solving the followingequations:

${P_{1} = {P_{0} + \frac{P_{W}}{W_{2}} + \frac{P_{L}}{L_{2}} + \frac{P_{P}}{W_{2} \times L_{2}}}},{P_{2} = {P_{0} + \frac{P_{W}}{W_{2}} + \frac{P_{L}}{L_{3}} + \frac{P_{P}}{W_{2} \times L_{3}}}},{P_{3} = {P_{0} + \frac{P_{W}}{W_{3}} + \frac{P_{L}}{L_{2}} + \frac{P_{P}}{W_{3} \times L_{2}}}},{and}$$P_{4} = {P_{0} + \frac{P_{W}}{W_{3}} + \frac{P_{L}}{L_{3}} + {\frac{P_{P}}{W_{3} \times L_{3}}.}}$

With P₀, P_(W), P_(L), and P_(P) solved, the model parameter P in theB-type subregion 351 can be written as:

${P = {P_{0} + \frac{P_{W}}{W_{2}} + \frac{P_{L}}{L} + \frac{P_{P}}{W_{2} \times L}}};$the model parameter P in the B-type subregion 353 can be written as:

${P = {P_{0} + \frac{P_{W}}{W} + \frac{P_{L}}{L_{2}} + \frac{P_{P}}{W \times L_{2}}}};$the model parameter P in the B-type subregion 357 can be written as:

${P = {P_{0} + \frac{P_{W}}{W} + \frac{P_{L}}{L_{3}} + \frac{P_{P}}{W \times L_{3}}}};$and the model parameter P in the B-type subregion 359 can be written as:

$P = {P_{0} + \frac{P_{W}}{W_{3}} + \frac{P_{L}}{L} + {\frac{P_{P}}{W_{3} \times L}.}}$

This way, the parameter P is continuous when device width is varied fromany subregion to any other subregion in the geometrical space 300. Thus,the method in one embodiment of the present invention combines theadvantages of global models and binning models. In one aspect, themethod in one embodiment of the present invention attains the advantageof accuracy associated with binning models by dividing the devicegeometrical space into subregions and by generating a separate model foreach subregion. In another aspect, the method in one embodiment of thepresent invention provides prediction capabilities associated withglobal models in device geometry subregions for which global models aregenerated.

The forgoing descriptions of specific embodiments of the presentinvention are presented for purpose of illustration and description.They are not intended to be exhaustive or to limit the invention to theprecise forms disclosed, obviously many modifications and variations arepossible in view of the above teachings. The embodiments were chosen anddescribed in order to best explain the principles of the invention andits practical applications, to thereby enable others skilled in the artto best utilize the invention and various embodiments with variousmodifications as are suited to the particular use contemplated.Furthermore, the order of the steps in the method are not necessarilyintended to occur in the sequence laid out. It is intended that thescope of the invention be defined by the following claims and theirequivalents.

APPENDIX A MODEL PARAMETER LIST Symbol Symbol used in used in Notes(below equation Simulator Description Unit Default the table) MODELCONTROL PARAMETERS None level Level 9 for BSIM3SOI — 9 — Shmod shModFlag for self-heating — 0 0 - no self-heating, 1 - self-heating Mobmodmobmod Mobility model selector — 1 — Capmod capmod Flag for the shortchannel capacitance model — 2 nI-1 Noimod noimod Flag for Noise model —1 — PROCESS PARAMETERS t_(si) Tsi Silicon film thickness m 10⁻⁷ —t_(box) Tbox Buried oxide thickness m 3 × 10⁻⁷ — T_(ox) Tox Gate oxidethickness m 1 × 10⁻⁸ — X_(j) Xj S/D junction depth m nI-2 — n_(ch) NchChannel doping concentration 1/cm³ 1.7 × 10¹⁷ — n_(sub) Nsub Substratedoping concentration 1/cm³ 6 × 10¹⁶ nI-3 Ngate ngate poly gate dopingconcentration 1/cm³ 0 — DC PARAMETERS V_(th0) vth0 Threshold voltage@Vbs = 0 for long and — 0.7 — wide device K₁ k1 First order body effectcoefficient V^(1/2) 0.6 — K_(1w1) k1w1 First body effect width dependentm 0 — parameter K_(1w2) k1w2 Second body effect width dependent m 0 —parameter K₂ k2 Second order body effect coefficient — 0 — K₃ k3 Narrowwidth coefficient — 0 — K_(3b) k3b Body effect coefficient of k3 1/V 0 —K_(b1) Kb1 Backgate body charge coefficient — 1 — W₀ w0 Narrow widthparameter m 0 — N_(LX) nlx Lateral non-uniform doping parameter m1.74e−7 D_(vt0) Dvt0 first coefficient of short-channel effect — 2.2 —on Vth D_(vt1) dvt1 Second coefficient of short-channel — 0.53 — effecton Vth D_(vt2) dvt2 Body-bias coefficient of short-channel 1/V −0.032 —effect on Vth D_(vt0w) dvt0w first coefficient of narrow width effect —0 — on Vth for small channel length D_(vt1w) dvt1w Second coefficient ofnarrow width — 5.3e6 — effect on Vth for small channel length D_(vt2w)dvt2w Body-bias coefficient of narrow width 1/V −0.032 — effect on Vthfor small channel length μ₀ u0 Mobility at Temp = Tnom cm²/(V-sec) 670 —NMOSFET 250 PMOSFET U_(a) ua First-order mobility degradation m/V2.25e−9 — coefficient U_(b) ub Second-order mobility degradation (m/V)²5.9e−19 — coefficient U_(c) uc Body-effect of mobility degradation 1/V−.0465 — coefficient v_(sat) vsat Saturation velocity at Temp = Tnomm/sec 8e4 — A0 a0 Bulk charge effect coefficient for — 1.0 — channellength A_(gs) ags Gate bias coefficient of A_(bulk) 1/V 0.0 — B0 b0 Bulkcharge effect coefficient for m 0.0 — channel width B1 b1 Bulk chargeeffect width offset m 0.0 — Keta keta Body-bias coefficient of bulkcharge V⁻¹ 0 — effect Ketas Ketas Surface potential adjustment for bulkV 0 — charge effect A₁ A1 First non-saturation effect parameter 1/V 0.0— A₂ A2 Second non-saturation effect parameter 0 1.0 — R_(dsw) rdswParasitic resistance per unit width Ω-μm^(Wr) 100 — Prwb prwb Bodyeffect coefficient of Rdsw 1/V 0 — Prwg prwg Gate bias effectcoefficient of Rdsw 1/V^(1/2) 0 — Wr wr Width offset from Weff for Rds —1 — calculation Nfactor nfactor Subthreshold swing factor — 1 — Wintwint Width offset fitting parameter from I–V m 0.0 — without bias Lintlint Length offset fitting parameter from I–V m 0.0 — without bias DWgdwg Coefficient of Weff'S gate dependence m/V 0.0 DWb dwb Coefficient ofWeff'S substrate body bias m/V^(1/2) 0.0 dependence DWbc Dwbc Widthoffset for body contact isolation m 0.0 edge V_(off) voff Offset voltagein the subthreshold region V −0.08 — for large W and L Eta0 eta0 DIBLcoefficient in subthreshold region — 0.08 — Etab etab Body-biascoefficient for the 1/V −0.07 — subthreshold DIBL effect D_(sub) dsubDIBL coefficient exponent — 0.56 — C_(it) cit Interface trap capacitanceF/m² 0.0 — C_(dsc) cdsc Drain/Source to channel coupling F/m² 2.4e−4 —capacitance C_(dscb) cdscb Body-bias sensitivty of C_(dsc) F/m² 0 —C_(dscd) cdscd Drain-bias sensitivty of C_(dsc) F/m 0 — P_(clm) pclmChannel length modulation parameter — 1.3 — P_(dibl1) pdibl1 Firstoutput resistance DIBL effect — .39 — correction parameter P_(dibl2)pdibl2 Second output resistance DIBL effect — 0.086 — correctionparameter D_(rout) drout L dependence coefficient of the DIBL — 0.56 —correction parameter in Rout Pvag pvag Gate dependence of Early voltage— 0.0 — δ delta Effective V_(ds) parameter 0.01 — α₀ alpha0 The firstparameter of impact ionization m/V 0.0 — current F_(bjtii) fbjtiiFraction of bipolar current affecting — 0.0 — the impact ionization β₀beta0 First V_(ds) dependent parameter of V⁻¹ 0 — impact ionizationcurrent β₁ beta1 Second V_(ds) dependent parameter of — 0 — impactionization current β₂ beta2 Third V_(ds) dependent parameter of V 0.1 —impact ionization current V_(dsatii0) vdsatii0 Nominal drain saturationvoltage at V 0.9 — threshold for impact ionization current T_(ii) tiiTemperature dependent parameter — 0 — for impact ionization currentL_(ii) lii Channel length dependent parameter — 0 — at threshold forimpact ionization current E_(satii) esatii Saturation channel electricfield for V/m 1e7 — impact ionization current S_(ii0) sij0 First V_(gs)dependent parameter for V⁻¹ 0.5 — impact ionization current Sii1 sii1Second V_(gs) dependent parameter for V⁻¹ 0.1 — impact ionizationcurrent Sii2 sii2 Third V_(gs) dependent parameter for V⁻¹ 0 — impactionization current S_(iid) siid dependent parameter of drain V⁻¹ 0 —saturation voltage for impact ionization current α_(gidl) Agidl GIDLconstant Ω⁻¹ 0.0 — β_(gidl) Bgidl GIDL exponential coefficient V/m 0.0 —χ Ngidl GIDL V_(ds) enhancement coefficient V 1.2 — n_(tun) Ntun Reversetunneling non-ideality factor — 10.0 — n_(diode) Ndio Diode non-idealityfactor — 1.0 — n_(recf0) Nrecf0 Recombination non-ideality factor at —2.0 — forward bias n_(recr0) Nrecr0 Recombination non-ideality factor at— 10 — reversed bias i_(sbjt) Isbjt BJT injection saturation currentA/m² 1e−6 — i_(sdif) Isdif Body to source/drain injection A/m² 1e−7 —saturation current i_(srec) Isrec Recombination in depletion saturationA/m² 1e-5 — current i_(stun) Istun Reverse tunneling saturation currentA/m² 0.0 — Ln Ln Electron/hole diffusion length m 2e−6 — V_(rec0) Vrec0Voltage dependent parameter for V 0 — recombination current V_(tun0)Vtun0 Voltage dependent parameter for V 0 — tunneling current N_(bjt)Nbjt Power coefficient of channel length — 1 — dependency for bipolarcurrent L_(bjt0) Lbjt0 Reference channel length for bipolar m 0.20e−6 —current V_(abjt) Vabjt Early voltage for bipolar current V 10 — A_(ely)Aely Channel length dependency of early V/m 0 — voltage for bipolarcurrent A_(hli) Ahli High level injection parameter for — 0 — bipolarcurrent Rbody Rbody Intrinsic body contact sheet resistance ohm/m² 0.0 —Rbsh Rbsh Extrinsic body contact sheet resistance ohm/m² 0.0 — Rsh rshSource drain sheet resistance in ohm per Ω/square 0.0 — square SymbolSymbol used in used in Notes (below equation SPICE Description UnitDefault the table) AC AND CAPACITANCE PARAMETERS Xpart xpart Chargepartitioning rate flag — 0 CGSO cgso Non LDD region source-gate overlapF/m calculated nC-1 capacitance per channel length CGDO cgdo Non LDDregion drain-gate overlap F/m calculated nC-2 capacitance per channellength CGEO cgeo Gate substrate overlap capacitance per F/m 0.0 — unitchannel length Cjswg cjswg Source/Drain (gate side) sidewall junctionF/m² 1e⁻¹⁰ — capacitance per unit width (normalized to 100 nm T_(si))Pbswg pbswg Source/Drain (gate side) sidewall junction V .7 —capacitance buit in potential Symbol Symbol used in used in Notes (belowequation Simulator Description Unit Default the table) AC ANDCAPACITANCE PARAMETERS Mjswg mjswg Source/Drain (gate side) sidewalljunction V 0.5 — capacitance grading coefficient t_(t) tt Diffusioncapacitance transit time second 1ps — coefficient N_(dif) Ndif Powercoefficient of channel length — 1 — dependency for diffusion capacitanceL_(dif0) Ldif0 Channel-length dependency coefficient — 1 — of diffusioncap. V_(sdfb) vsdfb Source/drain bottom diffusion V calculated nC-3capacitance flatband voltage V_(sdth) vsdth Source/drain bottomdiffusion V calculated nC-4 capacitance threshold voltage C_(sdmin)csdmin Source/drain bottom diffusion V calculated nC-5 minimumcapacitance A_(sd) asd Source/drain bottom diffusion — 0.3 — smoothingparameter C_(sdesw) csdesw Source/drain sidewall fringing F/m 0.0 —capacitance per unit length CGSl cgsl Light doped source-gate regionoverlap F/m 0.0 — capacitance CGDl cgdl Light doped drain-gate regionoverlap F/m 0.0 — capacitance CKAPPA ckappa Coefficient for lightlydoped region F/m 0.6 — overlap capacitance fringing field capacitance Cfcf Gate to source/drain fringing field F/m calculated nC-6 capacitanceCLC clc Constant term for the short channel model m 0.1 × 10⁻⁷ — CLE cleExponential term for the short channel none 0.0 — model DLC dlc Lengthoffset fitting parameter for gate m lint — charge DLCB dlcb Lengthoffset fitting parameter for body m lint — charge DLBG dlbg Lengthoffset fitting parameter for m 0.0 — backgate charge DWC dwc Widthoffset fitting parameter from C-V m wint — DelVt delvt Threshold voltageadjust for C-V V 0.0 — F_(body) fbody Scaling factor for body charge —1.0 — acde acde Exponential coefficient for charge m/V 1.0 — thicknessin capMod = 3 for accumulation and depletion regions. moin moinCoefficient for the gate-bias dependent V^(1/2) 15.0 — surfacepotential. Symbol Symbol used in used in equation Simulator DescriptionUnit Default Notes TEMPERATURE PARAMETERS Tnom tnom Temperature at whichparameters are expected ° C. 27 — μte ute Mobility temperature exponentnone −1.5 — Kt1 kt1 Temperature coefficient for threshold voltage V−0.11 — Kt11 kt11 Channel length dependence of the temperature V * m 0.0coefficient for threshold voltage Kt2 kt2 Body-bias coefficient of theVth temperature none 0.022 — effect Ua1 ua1 Temperature coefficient forU_(a) m/V 4.31e−9 — Ub2 ub1 Temperature coefficient for U_(b) (m/V)²−7.61e−18 — Uc1 uc1 Temperature coefficient for Uc 1/V −.056 nT-1 At atTemperature coefficient for saturation velocity m/sec 3.3e4 — Tcijswgtcjswg Temperature coefficient of C_(jswg) 1/K 0 — Tpbswg tpbswgTemperature coefficient of P_(bswg) V/K 0 — cth0 cth0 Normalized thermalcapacity m° C./ 0 — (W * sec) Prt prt Temperature coefficient for RdswΩ-μm 0 — Rth0 rth0 Normalized thermal resistance m° C./W 0 — Nt_(recf)Ntrecf Temperature coefficient for N_(recf) — 0 — Nt_(recr) NtrecrTemperature coefficient for N_(recr) — 0 — X_(bjt) xbjt Power dependenceof j_(bjt) on temperature — 2 — X_(dif) xdif Power dependence of j_(dir)on temperature — 2 — X_(rec) xrec Power dependence of j_(rec) ontemperature — 20 — X_(tun) xtun Power dependence of j_(tun) ontemperature — 0 — NOTES nI-1. BSJIMPD2.0 supports capmod = 2 and 3 only.Capmod = 0 and 1 are not supported. nI-2. In modem SOI technology,source/drain extension or LDD are commonly used. As a result, thesource/drain junction depth (X_(j)) can be different from the siliconfilm thickness (T_(si)). By default, if X_(j) is not given, it is set toT_(si). X_(j) is not allowed to be greater than T_(si). nI-3. BSIMPDrefers substrate to the silicon below buried oxide, not the well regionin BSIM3. It is used to calculate backgate flatband voltage (V_(fbb))and parameters related to source/drain diffusion bottom capacitance(V_(sdth), V_(sdfb), C_(sdmin)). Positive n_(sub) means the same type ofdoping as the body and negative n_(sub) means opposite type of doping.nC-1. If cgso is not given then it is calculated using: if (dlc is givenand is greater 0) then,    cgso = p1 = (dlc * cox) − cgs1 if (thepreviously calculated cgso < 0), then    cgso = 0 else cgso = 0.6 *Tsi * cox nC-2. Cgdo is calculated in a way similar to Csdo nC-3. If(n_(sub) is positive) $\begin{matrix}\; & {V_{sdfb} = {{{- \frac{k\; T}{q}}{\log( \frac{10^{20} \cdot n_{sub}}{n_{i} \cdot n_{i}} )}} - 0.3}} \\{else} & \; \\\; & {V_{sdfb} = {{{- \frac{k\; T}{q}}{\log( \frac{10^{20}}{n_{sub}} )}} + 0.3}}\end{matrix}\quad$ nC-4. If (n_(sub) is positive)${\phi_{sd} = {2\frac{k\; T}{q}{\log( \frac{n_{sub}}{n_{i}} )}}},{\gamma_{sd} = \frac{5.753 \times 10^{- 12}\sqrt{n_{sub}}}{C_{box}}}$

I.  BSIMPD  IV 1  Body  VoltagesV_(bsh)  is  equal  to  the  V_(bs)  bounded  between  (V_(bsc), ϕ_(s1)).  V_(bsh)  is  used  in  V_(th)  and  A_(bulk)  calculation${{1.1\mspace{14mu} T\; 1} = {V_{bsc} + {0.5\lbrack {V_{bs} - V_{bsc} - \delta + \sqrt{( {V_{bs} - V_{bsc} - \delta} )^{2} - {4\delta\; V_{bsc}}}} \rbrack}}},{V_{bsc} = {{- 5}\mspace{14mu} V}}$${{1.2\mspace{14mu} V_{bsh}} = {\phi_{s1} - {0.5\lbrack {\phi_{s1} - {T\; 1} - \delta + \sqrt{( {\phi_{s1} - {T\; 1} - \delta} )^{2} - {4\delta\; T_{1}}}} \rbrack}}},{\phi_{s1} = 1.5}$${{V_{bsh}\mspace{14mu}{is}\mspace{14mu}{further}\mspace{14mu}{limited}\mspace{14mu}{to}\mspace{14mu} 0.95\phi_{s}\mspace{14mu}{to}\mspace{14mu}{give}\mspace{14mu}{V_{bseff}.1.3}\mspace{14mu} V_{bseff}} = {\phi_{s0} - {0.5\lbrack {\phi_{s0} - V_{bsh} - \delta + \sqrt{( {\phi_{s0} - V_{bsh} - \delta} )^{2} + {4{\delta V}_{bsh}}}} \rbrack}}},{\phi_{s0} = {0.95\phi_{s}}}$2.  Effective  Channel   Length   and  Width${2.1\mspace{14mu} d\; W^{\prime}} = {W_{\ln} + \frac{W_{l}}{L^{W_{\ln}}} + \frac{W_{w}}{W^{W_{wn}}} + \frac{W_{wl}}{L^{W_{ln}}W^{W_{wn}}}}$${2.2\mspace{14mu} d\; W} = {{d\; W^{\prime}} + {d\; W_{g}V_{gsteff}} + {d\;{W_{b}( {\sqrt{\Phi_{x} - V_{bseff}} - \sqrt{\Phi_{x}}} )}}}$${2.3\mspace{14mu} d\; L} = {L_{int} + \frac{L_{l}}{L^{L_{in}}} + \frac{L_{w}}{W^{L_{wn}}} + \frac{L_{wl}}{L^{L_{in}}W^{L_{wn}}}}$2.4  L_(eff) = L_(drawn) − 2d L2.5  W_(eff) = W_(drown) − N_(bc)d W_(bc) − (2 − N_(bc))d W2.6  W_(eff)^(′) = W_(drawn) − N_(bc)d W_(bc) − (2 − N_(bc))d W^(′)${2.7\mspace{14mu} W_{diod}} = {\frac{W_{eff}^{\prime}}{N_{seg}} + P_{dbcp}}$${2.8\mspace{14mu} W_{dias}} = {\frac{W_{eff}^{\prime}}{N_{seg}} + P_{shcp}}$3.  Threshold  Voltage${3.1\mspace{14mu} V_{th}} = {V_{tho} + {K_{1{eff}}( {{sqrtPhisExt} - \sqrt{\Phi_{s}}} )} - {K_{2}V_{bseff}} + {{K_{1{eff}}( {\sqrt{1 + \frac{N_{LX}}{L_{eff}}} - 1} )}\sqrt{\Phi_{s}}} + {( {K_{3} + {K_{3b}V_{bseff}}} )\frac{T_{ox}}{W_{eff}^{\prime} + W_{o}}\Phi_{s}} - {{D_{{VT}\; 0\; w}( {{\exp( {{- D_{{VT}\; 1w}}\frac{W_{eff}^{\prime}L_{eff}}{2l_{tw}}} )} + {2{\exp( {{- D_{{VT}\; 1w}}\frac{W_{eff}^{\prime}L_{eff}}{l_{tw}}} )}}} )}( {V_{bi} - \Phi_{s}} )} - {{D_{{VT}\; 0}( {{\exp( {{- D_{{VT}\; 1}}\frac{L_{eff}}{2l_{t}}} )} + {2{\exp( {{- D_{VT1}}\frac{L_{eff}}{l_{l}}} )}}} )}( {V_{bi} - \Phi_{s}} )} - {( {{\exp( {{- D_{sub}}\frac{L_{eff}}{2l_{to}}} )} + {2{\exp( {{- D_{sub}}\frac{L_{eff}}{l_{to}}} )}}} )( {E_{tao} + {E_{sub}V_{bseff}}} )V_{ds}}}$${3.2\mspace{14mu} l_{t}} = {\sqrt{ɛ_{si}X_{dep}I\; C_{ox}}( {1 + {D_{{VT}\; 2}V_{besff}}} )}$$3.3,{{3.4\mspace{14mu}{sqrtPhisExt}} = {\sqrt{\phi_{s} - V_{besff}} + {s( {V_{bsh} - V_{bseff}} )}}},{s = {- \frac{1}{2\sqrt{\phi_{s} - \phi_{s\; 0}}}}}$${3.5\mspace{14mu} K_{1{eff}}} = {K_{1}( {1 + \frac{K_{1{w1}}}{W_{eff}^{\prime} + K_{1{w2}}}} )}$$3.6,{{3.7\mspace{14mu} l_{tw}} = {{\sqrt{ɛ_{si}{X_{dep}/C_{ox}}}( {1 + {D_{{VT}\; 2w}V_{besff}}} )\mspace{31mu} l_{to}} = \sqrt{ɛ_{si}{X_{{dep}\; 0}/C_{ox}}}}}$$3.8,{{3.9\mspace{14mu} X_{dep}} = {{\sqrt{\frac{2{ɛ_{si}( {\Phi_{s} - V_{besff}} )}}{q\; N_{ch}}}\mspace{31mu} X_{{dep}\; 0}} = \sqrt{\frac{2ɛ_{si}\Phi_{x}}{q\; N_{ch}}}}}$${3.10\mspace{14mu} V_{bi}} = {v_{t}{\ln( \frac{N_{ch}N_{DS}}{n_{i}^{2}} )}}$4.  Polydepletion  effect${{4.1\mspace{14mu} V_{poly}} + {\frac{1}{2}X_{poly}E_{poly}}} = \frac{q\; N_{gate}X_{poly}^{2}}{2\; ɛ_{si}}$${4.2\mspace{14mu} ɛ_{ox}E_{ox}} = {{ɛ_{si}E_{poly}} = \sqrt{2q\; ɛ_{si}N_{gate}V_{poly}}}$4.3  V_(gs) − V_(FB) − ϕ_(x) = V_(poly) + V_(ox)4.4  a(V_(gs) − V_(FB) − ϕ_(s) − V_(poly))² − V_(poly) = 0${4.5\mspace{14mu} a} = \frac{ɛ^{2}}{2q\; ɛ_{si}N_{gate}T_{ox}^{2}}$${4.6\mspace{14mu} V_{gs\_ off}} = {V_{FB} + \phi_{s} + {\frac{q\; ɛ_{si}N_{gate}T_{ox}^{2}}{ɛ_{ox}^{2}}\lbrack {\sqrt{1 + \frac{2{ɛ_{ox}^{2}( {V_{gs} - V_{FB} - \phi_{s}} )}}{q\; ɛ_{si}N_{gate}T_{ox}^{2}}} - 1} \rbrack}}$5.  Effective  V_(gst)  for  all  region  (with  Polysilicon  Depletion  Effect)${5.1\mspace{14mu} V_{gsteff}} = \frac{2n\; v_{t}{\ln\lbrack {1 + {\exp( \frac{V_{gs\_ eff} - V_{th}}{2n\; v_{t}} )}} \rbrack}}{1 + {2n\; C_{ox}\sqrt{\frac{2\Phi_{s}}{q\; ɛ_{si}N_{ch}}}{\exp( {- \frac{V_{gs\_ eff} - V_{th} - {2V_{off}}}{2n\; v_{t}}} )}}}$${5.2\mspace{14mu} n} = {1 + {N_{factor}\frac{ɛ_{si}/X_{dep}}{C_{ox}}} + \frac{( {C_{dsc} + {C_{dscd}V_{ds}} + {C_{dsch}V_{bseff}}} )\lbrack {{\exp( {{- D_{{VT}\; 1}}\frac{L_{eff}}{2l_{t}}} )} + {2{\exp( {{- D_{{VT}\; 1}}\frac{L_{eff}}{l_{t}}} )}}} \rbrack}{C_{ox}} + \frac{C_{it}}{C_{ox}}}$6.  Effective  Bulk  Charge  Factor${6.1\mspace{14mu} A_{bulk}} = {1 + ( {\frac{K_{1{eff}}}{2\sqrt{( {\phi_{s} + {Ketas}} ) - \frac{V_{bsh}}{1 + {{Keta} \cdot V_{bsh}}}}}( {{\frac{A_{0}L_{eff}}{L_{eff} + {2\sqrt{T_{si}X_{dep}}}}( {1 - {A_{gs}{V_{gsteff}( \frac{L_{eff}}{L_{eff} + {2\sqrt{T_{si}X_{dep}}}} )}^{2}}} )} + \frac{B_{0}}{W_{eff}^{\prime} + B_{1}}} )} )}$6.2  A_(bulk 0) = A_(bulk)(V_(gsteff) = 0)7.  Mobility  and  Saturation  Velocity 7.1  For  Mobmod = 1$\mu_{eff} = \frac{\mu_{o}}{1 + {( {U_{a} + {U_{c}V_{bseff}}} )( \frac{V_{gsteff} + {2V_{th}}}{T_{ox}} )} + {U_{b}( \frac{V_{gsteff} + {2V_{th}}}{T_{ox}} )}^{2}}$7.2  For  Mobmod = 2$\mu_{eff} = \frac{\mu_{o}}{1 + {( {U_{a} + {U_{c}V_{bseff}}} )( \frac{V_{gsteff}}{T_{ox}} )} + {U_{b}( \frac{V_{gsteff}}{T_{ox}} )}^{2}}$7.3  For  Mobmod = 3$\mu_{eff} = \frac{\mu_{0}}{1 + {\lbrack {{U_{a}( \frac{V_{gstef} + {2V_{th}}}{T_{ox}} )} + {U_{b}( \frac{V_{gsteff} + {2V_{th}}}{T_{ox}} )}^{2}} \rbrack( {1 + {U_{c}V_{bseff}}} )}}$8.  Drain  Saturation  Voltage 8.1  For  R_(ds) > 0  or  λ ≠ 1:${{8.1.a}\mspace{14mu} V_{dsat}} = \frac{{- b} - \sqrt{b^{2} - {4a\; c}}}{2a}$${{8.1.b}\mspace{14mu} a} = {{A_{bulk}^{2}W_{eff}v_{sat}C_{ox}R_{ds}} + {( {\frac{1}{\lambda} - 1} )A_{bulk}}}$${{8.1.c}\mspace{14mu} b} = {- \lbrack {{( {V_{gsteff} + {2v_{t}}} )( {\frac{2}{\lambda} - 1} )} + {A_{bulk}E_{sat}L_{eff}} + {3{A_{bulk}( {V_{gsteff} + {2v_{t}}} )}W_{eff}v_{sat}C_{ox}R_{ds}}} \rbrack}$8.1.d  c = (V_(gsteff) + 2v_(t))E_(sat)L_(eff) + 2(V_(gsteff) + 2v_(t))²W_(eff)v_(sat)C_(ox)R_(ds)8.1.e  λ = A₁V_(gsteff) + A₂${{8.2\mspace{14mu}{For}\mspace{14mu} R_{ds}} = 0},{\lambda = {{1:{{8.2.a}\mspace{14mu} V_{dsat}}} = \frac{E_{sat}{L_{eff}( {V_{gsteff} + {2v_{t}}} )}}{{A_{bulk}E_{sat}L_{eff}} + ( {V_{gsteff} + {2v_{t}}} )}}}$${{8.2.b}\mspace{14mu} E_{sat}} = \frac{2v_{sat}}{\mu_{eff}}$8.3  V_(dseff)$V_{dseff} = {V_{dsat} - {\frac{1}{2}\lbrack {V_{dsat} - V_{ds} - \delta + \sqrt{( {V_{dsat} - V_{dt} - \delta} )^{2} + {4\delta\; V_{dsat}}}} \rbrack}}$9.  Drain  Current  Expression${9.1\mspace{14mu} I_{{ds},{MOSFET}}} = {\frac{1}{N_{seg}}\frac{I_{{ds}\; 0}( V_{dseff} )}{1 + \frac{R_{ds}{I_{dso}( V_{dseff} )}}{V_{dseff}}}( {1 + \frac{V_{ds} - V_{dseff}}{V_{A}}} )}$${9.2\mspace{14mu}\beta} = {\mu_{eff}C_{ox}\frac{W_{eff}}{L_{eff}}}$${9.3\mspace{14mu} I_{dso}} = \frac{\beta\;{V_{gsteff}( {1 - {A_{bulk}\frac{V_{dseff}}{2( {V_{gsteff} + {2v_{t}}} )}}} )}V_{dseff}}{1 + \frac{V_{dseff}}{E_{sat}L_{eff}}}$${9.4\mspace{14mu} V_{A}} = {V_{Asat} + {( {1 + \frac{P_{vag}V_{gsteff}}{E_{sat}L_{eff}}} )( {\frac{1}{V_{ACLM}} + \frac{1}{V_{ADIBLC}}} )^{- 1}}}$${9.5\mspace{14mu} V_{ACLM}} = {\frac{{A_{bulk}E_{sat}L_{eff}} + V_{gsteff}}{P_{clm}A_{bulk}E_{sat}{litl}}( {V_{ds} - V_{dseff}} )}$${9.6\mspace{14mu} V_{ADIBLC}} = {\frac{( {V_{gseff} + {2v_{t}}} )}{\theta_{rout}( {1 + {P_{DIBLCB}V_{bseff}}} )}( {1 - \frac{A_{bulk}V_{dsat}}{{A_{bulk}V_{dsat}} + {2v_{t}}}} )}$$9.7\mspace{14mu}\theta_{rout}{P_{{DIBLC}\; 1}\lbrack {{{{\exp( {{{- D_{ROUT}}\frac{L_{eff}}{2l_{t\; 0}}} + {2{\exp( {{- D_{ROUT}}\frac{L_{eff}}{l_{t\; 0}}} )}}} \rbrack} + {P_{{DIBLC}\; 2}9.8\mspace{14mu} V_{Asat}}} = {{\frac{{E_{sat}L_{eff}} + V_{dsat} + {2R_{ds}v_{sat}C_{ox}W_{eff}{V_{gsteff}\lbrack {1 - \frac{A_{bulk}V_{dsat}}{2( {V_{gsteff} + {2v_{t}}} )}} \rbrack}}}{{2/\lambda} - 1 + {R_{ds}v_{sat}C_{ox}W_{eff}A_{bulk}}}9.9\mspace{14mu}{litl}} = {{\sqrt{\frac{ɛ_{si}T_{ox}T_{Si}}{ɛ_{ox}}}9.10\mspace{14mu} A_{bulk}} = {{1 + {( {\frac{K_{1{eff}}}{2\sqrt{( {\phi_{s} + {Ketas}} ) - \frac{V_{bsh}}{1 + {{Keta} \cdot V_{bsh}}}}}( {{\frac{A_{0}L_{eff}}{L_{eff} + {2\sqrt{T_{si}X_{dep}}}}( {1 - {A_{gs}{V_{gsteff}( \frac{L_{eff}}{L_{eff} + {2\sqrt{T_{si}X_{dep}}}} )}^{2}}} )} + \frac{B_{0}}{W_{eff}^{\prime} + B_{1}}} )} )10.\mspace{14mu}{Drain}\text{/}{Source}\mspace{14mu}{Resistance}10.1\mspace{14mu} R_{ds}}} = {{R_{dsw}\frac{1 + {P_{rwg}V_{gsteff}} + {P_{rwb}( {\sqrt{\phi_{s} - V_{bseff}} - \sqrt{\phi_{s}}} )}}{( {10^{6}W_{eff}^{\prime}} )^{Wr}}11.\mspace{14mu}{Impact}\mspace{14mu}{Ionization}\mspace{14mu}{Current}11.1\mspace{14mu} I_{ii}} = {{{\alpha_{0}( {I_{{ds},{MOSFET}} + {F_{hjtii}I_{c}}} )}{\exp( \frac{V_{diff}}{\beta_{2} + {\beta_{1}V_{diff}} + {\beta_{0}V_{diff}^{2}}} )}11.2\mspace{14mu} V_{diff}} = {{V_{ds} - {V_{dsatii}11.3\mspace{14mu} V_{dsatii}}} = {{{VgsStep} + {\lbrack {{V_{{dsatii}\; 0}( {1 + {T_{ii}( {\frac{T}{T_{nom}} - 1} )}} )}\frac{L_{ii}}{L_{eff}}} \rbrack 11.4\mspace{14mu}{VgsStep}}} = {( \frac{E_{satii}L_{eff}}{1 + {E_{satii}L_{eff}}} )( {\frac{1}{1 + {S_{{ii}\; 1}V_{gsteff}}} + S_{{ii}\; 2}} )( \frac{S_{{ii}\; 0}V_{gst}}{1 + {S_{iid}V_{ds}}} )12.\mspace{14mu}{Gate}\text{-}{induced}\text{-}{Drain}\text{-}{Leakage}\mspace{14mu}({GIDL})12.1\mspace{14mu}{At}\mspace{14mu}{drain}}}}}}}}}},{I_{dgidl} = {W_{diod}\alpha_{gidl}E_{s}{\exp( {- \frac{\beta_{gidl}}{E_{s}}} )}}},{E_{s} = {\frac{V_{ds} - V_{gs} - \chi}{3T_{ox}}12.2\mspace{14mu}{At}\mspace{14mu}{source}}},{I_{sgidl} = {W_{dios}\alpha_{gidl}E_{s}{\exp( {- \frac{\beta_{gidl}}{E_{s}}} )}}},{E_{s} = {\frac{{- V_{gs}} - \chi}{3T_{ox}}{If}\mspace{14mu} E_{s}\mspace{14mu}{is}\mspace{14mu}{negative}}},{{I_{gidl}\mspace{14mu}{is}\mspace{14mu}{set}\mspace{14mu}{to}\mspace{14mu}{zero}\mspace{14mu}{for}\mspace{14mu}{both}\mspace{14mu}{drain}\mspace{14mu}{and}\mspace{14mu}{{source}.13.}\mspace{14mu}{Body}\mspace{14mu}{Contact}\mspace{14mu}{Current}13.1\mspace{14mu} R_{bp}} = {R_{{body}\; 0}\frac{W_{eff}^{\prime}/N_{seg}}{L_{eff}}}},{R_{bodyext} = {{R_{bsh}N_{rb}13.2\mspace{14mu}{For}\mspace{14mu} 4} - {T\mspace{14mu}{device}}}},{I_{bp} = {{013.3\mspace{14mu}{For}\mspace{14mu} 5} - {T\mspace{14mu}{device}}}},{I_{bp} = {{\frac{V_{bp}}{R_{bp} + R_{bodytext}}14.\mspace{14mu}{Diode}\mspace{14mu}{and}\mspace{14mu}{BJT}\mspace{14mu}{currents}14.1\mspace{14mu}{Bipolar}\mspace{14mu}{Transport}\mspace{14mu}{Factor}\mspace{14mu}\alpha_{bjt}} = {{{\exp\lbrack {{- 0.5}( \frac{L_{eff}}{L_{n}} )^{2}} \rbrack}14.2\mspace{14mu}{Body}\text{-}{to}\text{-}{source}\text{/}{drain}\mspace{14mu}{diffusion}{14.2.a}\mspace{14mu} I_{{bs}\; 1}} = {{W_{dios}T_{si}{j_{sdif}( {{\exp( \frac{V_{bs}}{n_{dio}V_{t}} )} - 1} )}{14.2.b}\mspace{14mu} I_{{bd}\; 1}} = {{W_{diod}T_{si}{j_{sdif}( {{\exp( \frac{V_{bd}}{n_{dio}V_{t}} )} - 1} )}{14.3.\mspace{14mu}{Recombination}}\text{/}{trap}\text{-}{assist}\mspace{14mu}{tunneling}\mspace{14mu}{current}\mspace{14mu}{in}\mspace{14mu}{depletion}\mspace{14mu}{region}{14.3.a}\mspace{14mu} I_{{bs}\; 2}} = {{W_{dios}T_{si}{j_{srec}( {{\exp( \frac{V_{bs}}{0.026\mspace{14mu} n_{recf}} )} - {\exp( {\frac{V_{sb}}{0.026\mspace{14mu} n_{recr}}\frac{V_{{rec}\; 0}}{V_{{rec}\; 0} + V_{sb}}} )}} )}{14.3.b}\mspace{14mu} I_{{bd}\; 2}} = {{W_{diod}T_{si}{j_{srec}( {{\exp( \frac{V_{bd}}{0.026\mspace{14mu} n_{recf}} )} - {\exp( {\frac{V_{db}}{0.026\mspace{14mu} n_{recr}}\frac{V_{{rec}\; 0}}{V_{{rec}\; 0} + V_{db}}} )}} )}14.4\mspace{14mu}{Reverse}\mspace{14mu}{bias}\mspace{14mu}{tunneling}\mspace{14mu}{leakage}{14.4.a}\mspace{14mu} I_{{bs}\; 4}} = {{W_{dios}T_{si}{j_{stun}( {1 - {\exp( \frac{n_{tun}V_{sb}}{V_{{tun}\; 0} + V_{sb}} )}} )}{14.4.b}\mspace{14mu} I_{{bd}\; 4}} = {{W_{diod}T_{si}{j_{stun}( {1 - {\exp( \frac{n_{tun}V_{db}}{V_{{tun}\; 0} + V_{db}} )}} )}{14.5.\mspace{14mu}{Recombination}}\mspace{14mu}{current}\mspace{14mu}{in}\mspace{14mu}{neutral}\mspace{14mu}{body}{14.5.a}\mspace{14mu} I_{{bs}\; 3}} = {{( {1 - \alpha_{bjt}} ){I_{en}\lbrack {{\exp( \frac{V_{bs}}{n_{dio}V_{t}} )} - 1} \rbrack}\frac{1}{\sqrt{E_{hlis} + 1}}{14.5.b}\mspace{14mu} I_{{bd}\; 3}} = {{( {1 - \alpha_{bjt}} ){I_{en}\lbrack {{\exp( \frac{V_{bd}}{n_{dio}V_{t}} )} - 1} \rbrack}\frac{1}{\sqrt{E_{hlid} + 1}}{14.5.c}\mspace{14mu} I_{en}} = {{\frac{W_{eff}^{\prime}}{N_{seg}}T_{si}{j_{sbjt}\lbrack {L_{bjt}( {\frac{1}{L_{eff}} + \frac{1}{L_{n}}} )} \rbrack}^{N_{bjt}}{14.5.d}\mspace{14mu} E_{hlis}} = {{{A_{hli\_ eff}\lbrack {{\exp( \frac{V_{bs}}{n_{dio}V_{t}} )} - 1} \rbrack}{14.5.e}\mspace{14mu} E_{hlid}} = {{{A_{hli\_ eff}\lbrack {{\exp( \frac{V_{bd}}{n_{dio}V_{t}} )} - 1} \rbrack}{14.5.f}\mspace{14mu} A_{hli\_ eff}} = {{A_{hli}{\exp\lbrack {\frac{- {E_{g}( {300K} }}{n_{dio}V_{t}}{X_{bjt}( {1 - \frac{T}{T_{nom}}} )}} \rbrack}14.6\mspace{14mu}{BJT}\mspace{14mu}{collector}\mspace{14mu}{current}14.6a\mspace{14mu} I_{c}} = {{\alpha_{bjt}I_{en}\{ {{\exp\lbrack \frac{V_{bs}}{n_{dio}V_{t}} \rbrack} - {\exp\lbrack \frac{V_{bd}}{n_{dio}V_{t}} \rbrack}} \}\frac{1}{E_{2{nd}}}{14.6.b}\mspace{14mu} E_{2{nd}}} = {{\frac{E_{ely} + \sqrt{E_{ely}^{2} + {4E_{hli}}}}{2}{14.6.c}\mspace{14mu} E_{ely}} = {{1 + {\frac{V_{bx} + V_{bd}}{V_{Abit} + {A_{ely}L_{eff}}}{14.6.d}\mspace{14mu} E_{hli}}} = {{E_{hlis} + {E_{hlio}14.7\mspace{14mu}{Total}\mspace{14mu}{body}\text{-}{source}\text{/}{drain}\mspace{14mu}{current}14.7a\mspace{14mu} I_{bs}}} = {{I_{{bs}\; 1} + I_{{bs}\; 2} + I_{{bs}\; 3} + {I_{{bs}\; 4}14.7b\mspace{14mu} I_{bd}}} = {{I_{bd1} + I_{{bd}\; 2} + I_{{bd}\; 3} + {I_{{bd}\; 4}15.\mspace{14mu}{Total}\mspace{14mu}{Body}\mspace{14mu}{Current}15.\; 1\mspace{11mu} I_{ii}} + I_{dgidl} + I_{sgidl} - I_{bs} - I_{bd} - I_{bp}} = {{016.\mspace{14mu}{Temperature}\mspace{14mu}{Effects}16.1\mspace{14mu} V_{{th}{(T)}}} = {{V_{{th}{({nom})}} + {( {K_{T1} + {K_{t\backslash l}/L_{eff}} + {K_{T2}V_{bseff}}} )( {{T/T_{nom}} - 1} )16.2\mspace{14mu}\mu_{o{(T)}}}} = {\mu_{o{({Tnom})}}( \frac{T}{T_{nom}} )}^{\mu\; i\; c}}}}}}}}}}}}}}}}}}}}}}}},{v_{{sat}{(T)}} = {{v_{{sat}{({Tnom})}} - {{A_{T}( {{T/T_{nom}} - 1} )}16.3\mspace{14mu} R_{{dsw}{(T)}}}} = {{{R_{{dsw}{({nom})}}T} + {{P_{rt}( {\frac{T}{T_{nom}} - 1} )}16.4\mspace{14mu} U_{a{(T)}}}} = {{U_{a{({Tnom})}} + {{U_{a1}( {{T/T_{nom}} - 1} )}16.5\mspace{14mu} U_{b{(T)}}}} = {{U_{b{({Tnom})}} + {{U_{b1}( {{T/T_{nom}} - 1} )}16.6\mspace{14mu} U_{c{(T)}}}} = {{U_{c{({Tnom})}} + {{U_{c1}( {{T/T_{nom}} - 1} )}16.7\mspace{14mu} R_{th}}} = \frac{R_{{th}\; 0}}{W_{eff}^{\prime}/N_{seg}}}}}}}},{C_{th} = {{C_{{th}\; 0}\frac{W_{eff}^{\prime}}{N_{seg}}16.8\mspace{14mu} j_{sbjt}} = {{j_{{sbjt}\; 0}{\exp\lbrack {\frac{- {E_{g}( {300K} )}}{n_{dio}V_{t}}{X_{bjt}( {1 - \frac{T}{T_{nom}}} )}} \rbrack}16.9\mspace{14mu} j_{sdif}} = {{j_{{sdif}\; 0}{\exp\lbrack {\frac{- {E_{g}( {300K} )}}{n_{dio}V_{t}}{X_{bjt}( {1 - \frac{T}{T_{nom}}} )}} \rbrack}16.10\mspace{11mu} j_{srec}} = {{j_{{srec}\; 0}{\exp\lbrack {\frac{- {E_{g}( {300K} )}}{n_{{recf}\; 0}V_{t}}{X_{{rec}\;}( {1 - \frac{T}{T_{nom}}} )}} \rbrack}16.11\mspace{11mu} j_{stun}} = {{j_{{stun}\; 0}{\exp\lbrack {X_{{tun}\;}( {\frac{T}{T_{nom}} - 1} )} \rbrack}16.12\mspace{14mu} n_{recf}} = {{{n_{recf0}\lbrack {1 + {n\;{t_{recf}( {\frac{T}{T_{nm}} - 1} )}}} \rbrack}16.13\mspace{14mu} n_{recr}} = {{n_{recr0}\lbrack {1 + {n\;{t_{recr}( {\frac{T}{T_{nm}} - 1} )}}} \rbrack}E_{g}\mspace{14mu}{is}\mspace{14mu}{the}\mspace{14mu}{energy}\mspace{14mu}{gap}\mspace{14mu}{{energy}.17.}\mspace{14mu}{Oxide}\mspace{14mu}{Tunneling}\mspace{14mu}{Current}17.1\mspace{14mu}{In}\mspace{14mu}{inversion}}}}}}}}},{{17.1.a.\mspace{14mu} J_{gb}} = {{A\;{\frac{V_{gb}V_{aux}}{T_{ox}^{2}}\lbrack \frac{T_{oxref}}{T_{oxqm}} \rbrack}^{N_{tun}}{\exp\lbrack \frac{{- {B( {\alpha_{{gb}\; 1} - {\beta_{{gb}\; 1}{V_{ox}}}} )}}T_{ox}}{1 - {{V_{ox}}/V_{{gb}\; 1}}} \rbrack}{17.1.b.\mspace{14mu} V_{aux}}} = {{V_{EVB}{\ln\lbrack {1 + {\exp( \frac{{V_{ox}} - \varphi_{g}}{V_{EVB}} )}} \rbrack}{17.1.c.\mspace{14mu} A}} = {{\frac{q^{3}}{8\pi\; h\;\phi_{b}}{17.1.d.\mspace{14mu} B}} = {{\frac{8\pi\sqrt{2m_{ox}}\phi_{b}^{3/2}}{3h\; q}{17.1.e.\mspace{14mu}\phi_{b}}} = {{4.2{eV}{17.1.f.\mspace{14mu} m_{ox}}} = {0.3m_{0}{17.2.\mspace{14mu}{In}}\mspace{14mu}{accumulation}}}}}}}},{{17.2{a.\mspace{14mu} J_{gb}}} = {{A\;{\frac{V_{gb}V_{aux}}{T_{ox}^{2}}\lbrack \frac{T_{oxref}}{T_{oxqm}} \rbrack}^{N_{tun}}{\exp\lbrack \frac{{- {B( {\alpha_{{gb}\; 2} - {\beta_{{gb}\; 2}{V_{ox}}}} )}}T_{ox}}{1 - {{V_{ox}}/V_{{gb}\; 2}}} \rbrack}{17.1.b.\mspace{14mu} V_{aux}}} = {{V_{ECB}V_{t}{\ln\lbrack {1 + {\exp( {- \frac{V_{gb} - V_{fb}}{V_{ECB}}} )}} \rbrack}{17.1.c.\mspace{14mu} A}} = {{\frac{q^{3}}{8\pi\; h\;\phi_{b}}{17.1.d.\mspace{14mu} B}} = {{\frac{8\pi\sqrt{2m_{ox}}\phi_{b}^{3/2}}{3h\; q}{17.1.e.\mspace{14mu}\phi_{b}}} = {{3.1e\; V{17.1.f.\mspace{14mu} m_{ox}}} = {{0.4\mspace{14mu} m_{0}{{II}.\mspace{14mu}{BSIMPD}}\mspace{14mu}{CV}18.\mspace{14mu}{Dimension}\mspace{14mu}{Dependence}18.1\mspace{14mu}\delta\; W_{eff}} = {{{DWC} + \frac{W_{lc}}{L^{W_{1a}}} + \frac{W_{wc}}{W^{W_{ww}}} + {\frac{W_{wlc}}{L^{W_{1n}}W^{W_{ww}}}18.2\mspace{14mu}\delta\; L_{eff}}} = {{{DLC} + \frac{L_{lc}}{L^{L_{1a}}} + \frac{L_{wc}}{W^{L_{ww}}} + {\frac{L_{wlc}}{L^{L_{\ln}}W^{L_{ww}}}18.3\mspace{14mu} L_{active}}} = {{L_{drawn} - {2\delta\; L_{eff}18.4\mspace{14mu} L_{activeB}}} = {{L_{active} - {{DLCB}18.5\mspace{14mu} L_{activeBG}}} = {{L_{activeB} + {2\;\delta\; L_{bg}18.6\mspace{14mu} W_{active}}} = {{W_{drawn} - {N_{bc}d\; W_{bc}} - {( {2 - N_{bc}} )\delta\; W_{eff}18.7\mspace{14mu} W_{diosCV}}} = {{\frac{W_{active}}{N_{seg}} + {P_{sbcp}18.8\mspace{14mu} W_{diodCV}}} = {{\frac{W_{active}}{N_{seg}} + {P_{dbcp}19.\mspace{20mu}{Charge}\mspace{14mu}{Conservation}19.1\mspace{14mu} Q_{Bf}}} = {{Q_{acc} + Q_{{sub}\; 0} + {Q_{subs}19.2\mspace{14mu} Q_{inv}}} = {{Q_{{inv},s} + {Q_{{inv},d}19.3\mspace{14mu} Q_{g}}} = {{{- ( {Q_{inv} + Q_{Bf}} )}19.4\mspace{14mu} Q_{b}} = {{Q_{Bf} - Q_{c} + Q_{js} + {Q_{jd}19.5\mspace{14mu} Q_{s}}} = {{Q_{{inv},s} - {Q_{js}19.6\mspace{14mu} Q_{d}}} = {{Q_{{inv},d} - {Q_{jd}19.7\mspace{14mu} Q_{g}} + Q_{c} + Q_{b} + Q_{s} + Q_{d}} = {{020\mspace{14mu}{Intrinsic}\mspace{14mu}{Charges}20.1\mspace{14mu}(1){capMod}} = {{2{20.1.a}\mspace{14mu}{Front}\mspace{14mu}{Gate}\mspace{14mu}{Body}\mspace{14mu}{Charge}{20.1.a}{.1}\mspace{14mu}{Accumulation}\mspace{14mu}{Charge}\text{}V_{FBeff}} = {{V_{fb} - {0.5( {( {V_{fb} - V_{gb} - \delta} ) + \sqrt{( {V_{fb} - V_{gb} - \delta} )^{2} + \delta^{2}}} )\mspace{14mu}{where}\mspace{14mu} V_{gb}}} = {{V_{gs} - {V_{bseff}{20.1.a}{.2}\mspace{14mu} V_{fb}}} = {{V_{th} - \phi_{s} - {K_{1{eff}}\sqrt{\phi_{s} - V_{bseff}}} + {{delvt}{20.1.a}{.3}\mspace{14mu} V_{gsteffCV}}} = {{n\; v_{t}{\ln( {1 + {{\exp\lbrack \frac{V_{gs} - V_{th}}{n\; v_{t}} \rbrack} \cdot {\exp\lbrack {- \frac{delvt}{n\; v_{t}}} \rbrack}}} )}{20.1.a}{.4}\mspace{14mu} Q_{acc}} = {{{- {F_{body}( {\frac{W_{active}L_{actioveB}}{N_{seg}} + A_{gbep}} )}}{C_{ox}( {V_{FBeff} - V_{fb}} )}{20.1.a}{.6}\mspace{14mu}{Gate}\mspace{14mu}{Induced}\mspace{14mu}{Depletion}\mspace{14mu}{Charge}\mspace{281mu} Q_{{sub}\; 0}} = {{{- {F_{body}( {\frac{W_{active}L_{actioveB}}{N_{seg}} + A_{gbep}} )}}C_{ox}\frac{K_{1{eff}}^{2}}{2}( {{- 1} + \sqrt{\frac{1 + {4( {V_{gs} - V_{FBeff} - V_{gsteffCV} - V_{bseff}} )}}{K_{teff}^{2}}}} ){20.1.a}{.7}\mspace{14mu} V_{dsatCV}} = {V_{gsteffCV}/A_{bulkCV}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},{{A_{bulkCV} = {{{A_{{bulk}\; 0}\lbrack {1 + ( \frac{CLC}{L_{activeB}} )^{CLE}} \rbrack}{20.1.a}{.9}\mspace{14mu} Q_{subs}} = {{{F_{body}( {\frac{W_{active}L_{activeB}}{N_{seg}} + A_{gbcp}} )}K_{1{eff}}{{C_{ox}( {A_{bulkCV} - 1} )}\lbrack {\frac{V_{dsCV}}{2} - \frac{A_{bulkCV}V_{dsCV}^{2}}{12( {V_{gsteffCV} - {A_{bulkCV}{V_{dsCV}/2}}} )}} \rbrack}{20.1.a}{.10}\mspace{14mu}{Back}\mspace{14mu}{Gate}\mspace{14mu}{Body}\mspace{14mu}{Charge}\text{}Q_{e}} = {{k_{b\; 1}{F_{body}( {\frac{W_{active}L_{activeBG}}{N_{seg}} + A_{ebcp}} )}{C_{box}( {V_{es} - V_{fbb} - V_{bseff}} )}{20.1.b}\mspace{14mu}{Inversion}\mspace{14mu}{Charge}{20.1.b}{.1}\mspace{14mu} V_{cveff}} = {{V_{{dsatt},{CV}} - {0.5( {V_{4} + \sqrt{V_{4}^{2} + {4\delta_{4}V_{{dsat},{CV}}}}} )\mspace{14mu}{where}\mspace{14mu} V_{4}}} = {V_{{dsat},{CV}} - V_{ds} - \delta_{4}}}}}}};{\delta_{4} = {{0.02{20.1.b}{.2}\mspace{14mu} Q_{inv}} = {{{- ( {\frac{W_{active}L_{active}}{N_{seg}} + A_{gbcp}} )}{C_{ox}( {( {V_{gsteffCV} - {\frac{A_{bulkCV}}{2}V_{cveff}^{2}}} ) + \frac{A_{bulkCV}^{2}V_{cveff}^{2}}{12( {V_{gsteffCV} - {\frac{A_{bulkCV}^{2}}{2}V_{cveff}}} )}} )}{20.1.b}{.3}\mspace{14mu} 50\text{/}50\mspace{14mu}{Charge}\mspace{14mu}{Partition}\text{}Q_{{inv},x}} = {Q_{{inv},d} = {{0.5\mspace{14mu} Q_{inv}{20.1.b}{.4}\mspace{14mu} 40\text{/}60\mspace{14mu}{Charge}\mspace{14mu}{Partition}\text{}Q_{{inv},x}} = {{{- \frac{( {\frac{W_{active}L_{active}}{N_{seg}} + A_{gbcp}} )C_{ox}}{2( {V_{gsteffCV} - {\frac{A_{bulkCV}}{2}V_{cveff}}} )^{2}}}( {V_{gsteffCV}^{3} - {\frac{4}{3}{V_{gsteffCV}^{2}( {A_{bulkCV}V_{cveff}} )}} + {\frac{2}{3}{V_{gsteff}( {A_{bulkCV}V_{cveff}} )}^{2}} - {\frac{2}{15}( {A_{bulkCV}V_{cveff}} )^{3}}} )Q_{{inv},d}} = {{{- \frac{( {\frac{W_{active}L_{active}}{N_{seg}} + A_{gbcp}} )C_{ox}}{2( {V_{gsteffCV} - {\frac{A_{bulkCV}}{2}V_{cveff}}} )^{2}}}( {V_{gsteffCV}^{3} - {\frac{5}{3}{V_{gsteffCV}^{2}( {A_{bulkCV}V_{cveff}} )}} + {V_{gsteff}( {A_{bulkCV}V_{cveff}} )}^{2} - {\frac{1}{5}( {A_{bulkCV}V_{cveff}} )^{3}}} ){20.1.b}{.6}\mspace{14mu} 0\text{/}100\mspace{14mu}{Charge}\mspace{14mu}{Partition}Q_{{inv},x}} = {{{- \frac{{W_{active}L_{active}} + A_{gbcp}}{N_{seg}}}{C_{ox}( {\frac{V_{gsteff}}{2} + \frac{A_{bulkCV}V_{cveff}}{4} - \frac{( {A_{bulkCV}V_{cveff}} )^{2}}{24( {V_{gsteffCV} - {\frac{A_{bulkCV}}{2}V_{cveff}}} )}} )}{20.1.b}{.7}\mspace{14mu} Q_{{inv},d}} = {{{- \frac{{W_{active}L_{active}} + A_{gbcp}}{N_{seg}}}{C_{ox}( {\frac{V_{gsteff}}{2} + \frac{3A_{bulkCV}V_{cveff}}{4} + \frac{( {A_{bulkCV}V_{cveff}} )^{2}}{8( {V_{gsteffCV} - {\frac{A_{bulkCV}}{2}V_{cveff}}} )}} )}20.2\mspace{14mu}(2){capMod}} = {{3( {{Charge}\text{-}{Thickness}\mspace{14mu}{Model}} ){capMod}} = {3\mspace{14mu}{only}\mspace{14mu}{supports}\mspace{14mu}{zero}\text{-}{bias}\mspace{14mu}{flat}\mspace{14mu}{band}\mspace{14mu}{voltage}}}}}}}}}}}}},{{{which}\mspace{14mu}{is}\mspace{14mu}{calculated}\mspace{14mu}{from}\mspace{14mu}{bias}\text{-}{independent}\mspace{14mu}{threshold}\mspace{14mu}{{voltage}.\text{}{This}}\mspace{14mu}{is}\mspace{14mu}{different}\mspace{14mu}{from}\mspace{14mu}{capMod}} = {2.\mspace{14mu}{For}\mspace{14mu}{the}\mspace{14mu}{finite}\mspace{14mu}{thickness}\mspace{14mu}( X_{DC} )\mspace{14mu}{formulation}}},{{refer}\mspace{14mu}{to}\mspace{14mu}{Chapter}\mspace{14mu} 4\mspace{14mu}{of}\mspace{14mu}{BSIM3v3}{.2}\mspace{14mu}{Users}}}’ }s\mspace{14mu}{{Manual}.20.2.a}\mspace{14mu}{Front}\mspace{14mu}{Gate}\mspace{14mu}{Body}\mspace{14mu}{Charge}$20.2.a.1  Accumulation  Charge$V_{FBeff} = {{V_{fb} - {0.5( {( {V_{fb} - V_{gb} - \delta} ) + \sqrt{( {V_{fb} - V_{gb} - \delta} )^{2} + \delta^{2}}} )\mspace{14mu}{where}\mspace{14mu} V_{gb}}} = {V_{gs} - V_{bseff}}}$${{20.2.a}{.2}\mspace{14mu} V_{fb}} = {V_{th} - \phi_{s} - {K_{1{eff}}\sqrt{\phi_{s} - V_{bseff}}}}$${{20.2.a}{.3}\mspace{14mu} Q_{acc}} = {{- {F_{body}( {\frac{W_{active}L_{activeB}}{N_{seg}} + A_{gbcp}} )}}C_{axteff}V_{gbace}}$${{20.2.a}{.4}\mspace{14mu} V_{gbace}} = {0.5( {V_{0} + \sqrt{V_{0}^{2} + {4\delta\; V_{fb}}}} )}$20.2.a.5  V₀ = V_(fb) + V_(bseff) − V_(gs) − δ${{20.2.a}{.6}\mspace{14mu} C_{oxeff}} = \frac{C_{ox}C_{cen}}{C_{ox} + C_{cen}}$20.2.a.7  C_(cen) = ɛ_(Si)/X_(DC)20.2.a.8  Gate  Induced  Depletion  Charge$Q_{{sub}\; 0} = {{- {F_{body}( {\frac{W_{active}L_{activeB}}{N_{seg}} + A_{gbcp}} )}}C_{axteff}\frac{K_{1{eff}}^{2}}{2}( {{{- 1} + {\sqrt{1 + \frac{4( {V_{gs} - V_{FBeff} - V_{gsteffCV} - V_{bseff}} )}{K_{1{eff}}^{2}}}{20.2.a}{.9}\mspace{14mu}{Drain}\mspace{14mu}{Induced}\mspace{14mu}{Depletion}\mspace{14mu}{Charge}V_{dsatCV}}} = {{{( {V_{gsteffCV} - \Phi_{\delta}} )/A_{bulkCV}}{20.2.a}{.10}\mspace{14mu}\Phi_{\delta}} = {\Phi_{s} = {{2\Phi_{B}} = {{v_{t}{\ln\lbrack {1 + \frac{V_{gsteffCV}( {V_{gstefCV} + {2K_{1{eff}}\sqrt{2\Phi_{B}}}} )}{{moinK}_{1{eff}}v_{t}^{2}}} \rbrack}{20.2.a}{.11}\mspace{14mu} v_{dsCV}} = {v_{dsatCV} - {\frac{1}{2}( {{V_{dsatCV} - v_{ds} - \delta + {\sqrt{ {( {v_{dsatCV} - v_{ds} - \delta} )^{2} + {4{\delta V}_{dsatCV}}} )}{20.2.a}{.12}\mspace{14mu} Q_{subs}}} = {{F_{body}( {\frac{W_{active}L_{activeB}}{N_{seg}} + A_{gbcp}} )}K_{1{eff}}{{C_{axeff}( {A_{bulkCV} - 1} )}\lbrack {{{\frac{V_{dsCV}}{2} - {\frac{A_{bulkCV}V_{dsCV}^{2}}{12( {V_{gsteffCV} - \Phi_{\delta} - {A_{bulkCV}{V_{dsCV}/2}}} )}{20.2.a}{.13}\mspace{14mu}{Back}\mspace{14mu}{Gate}\mspace{14mu}{Body}\mspace{14mu}{Charge}Q_{e}}} = {{k_{b\; 1}{F_{body}( {\frac{W_{active}L_{activeBG}}{N_{seg}} + A_{ebcp}} )}{C_{box}( {V_{es} - V_{fbb} - V_{bseff}} )}{20.2.b}\mspace{14mu}{Inversion}\mspace{14mu}{Charge}{20.2.b}{.1}\mspace{14mu} V_{cveff}} = {V_{{dsat},{CV}} - {0.5( {V_{4} + \sqrt{V_{4}^{2} + {4\delta_{4}V_{{dsat},{CV}}}}} )\mspace{14mu}{where}\mspace{14mu} V_{4}V_{{dsat},{CV}}} - V_{ds} - \delta_{4}}}};{\delta_{4} = {{0.02{20.2.b}{.2}\mspace{14mu} Q_{inv}} = {{{- ( {\frac{W_{active}L_{active}}{N_{seg}} + A_{gbcp}} )}{C_{axeff}( {( {V_{gsteffCV} - \Phi_{\delta} - {\frac{A_{bulkCV}}{2}V_{cveff}}} ) + \frac{A_{bulkCV}^{2}V_{cveff}^{2}}{12( {V_{gsteffCV} - \Phi_{\delta} - {\frac{A_{bulkCV}^{2}}{2}V_{cveff}}} )}} )}{20.2.b}{.3}\mspace{14mu} 50\text{/}50\mspace{14mu}{Charge}\mspace{14mu}{Partition}Q_{{inv},s}} = {Q_{{inv},d} = {{0.5Q_{inv}{20.2.b}{.4}\mspace{14mu} 40\text{/}60\mspace{14mu}{Charge}\mspace{14mu}{Partition}Q_{{inv},s}} = {{- \frac{( {\frac{W_{active}L_{active}}{N_{seg}} + A_{gbcp}} )C_{axeff}}{2( {V_{gsteffCV} - \Phi_{\delta} - {\frac{A_{bulkCV}}{2}V_{cveff}}} )^{2}}}( {( {V_{gsteffCV} - \Phi_{\delta}} )^{3} - {\frac{4}{3}( {V_{gsteffCV} - \Phi_{\delta}} )^{2}( {A_{bulkCV}V_{cveff}} )} + {\frac{2}{3}( {V_{gsteff} - \Phi_{\delta}} )( {A_{bulkCV}V_{cveff}} )^{2}} - {\frac{2}{15}( {{A_{bulkCV}V{20.2.b}{.5}Q_{{inv},d}} = {{- \frac{( {\frac{W_{active}L_{active}}{N_{seg}} + A_{gbcp}} )C_{axeff}}{2( {V_{gsteffCV} - \Phi_{\delta} - {\frac{A_{bulkCV}}{2}V_{cveff}}} )^{2}}}( {( {V_{gsteffCV} - \Phi_{\delta}} )^{3} - {\frac{5}{3}( {V_{gsteffCV} - \Phi_{\delta}} )^{2}( {A_{bulkCV}V_{cveff}} )} + {( {V_{gsteff} - \Phi_{\delta}} )( {A_{bulkCV}V_{cveff}} )^{2}} - {\frac{1}{5}( {{A_{bulkCV}V{20.2.b}{.6}\mspace{14mu} 0\text{/}100\mspace{14mu}{Charge}\mspace{14mu}{Partition}\mspace{365mu} Q_{{inv},s}} = {{\frac{{W_{active}L_{active}} + A_{gbcp}}{N_{seg}}{C_{oxeff}( {\frac{V_{gsteffCV} - \Phi_{\delta}}{2} + \frac{A_{bulkCV}V_{cveff}}{4} - \frac{( {A_{bulkCV}V_{cveff}} )^{2}}{24( {V_{gsteffCV} - \Phi_{\delta} - {\frac{A_{bulkCV}}{2}V_{cveff}}} )}} )}{20.2.b}{.7}\mspace{14mu} Q_{{inv},d}} = {{\frac{{W_{active}L_{active}} + A_{gbcp}}{N_{seg}}{C_{oxeff}( {\frac{V_{gsteffCV} - \Phi_{\delta}}{2} + \frac{3A_{bulkCV}V_{cveff}}{4} + \frac{( {A_{bulkCV}V_{cveff}} )^{2}}{8( {V_{gsteffCV} - \Phi_{\delta} - {\frac{A_{bulkCV}}{2}V_{cveff}}} )}} )}21\mspace{14mu}{Overlap}\mspace{14mu}{Capacitance}21.1{\mspace{11mu}\;}{Source}\mspace{14mu}{Overlap}\mspace{14mu}{Charge}21.1a\mspace{14mu} V_{gs\_ overlap}} = {{{\frac{1}{2}\{ {( {V_{gs} + \delta} ) + \sqrt{( {V_{gs} + \delta} )^{2} + {4\delta}}} \}\mspace{140mu} 21.1b\mspace{14mu}\frac{Q_{{overlap}.s}}{W_{diosCV}}{CGS}\;{0 \cdot V_{gs}}} + {{CGS}\; 1\{ {V_{gs} - V_{gs\_ overlap} + {\frac{CKAPPA}{2}( {{- 1} + \sqrt{1 + \frac{4V_{gs\_ overlap}}{CKAPPA}}} )}} \} 21.2{\mspace{11mu}\;}{Drain}\mspace{14mu}{Overlap}\mspace{14mu}{Charge}21.2a\mspace{14mu} V_{gd\_ overlap}}} = {{\frac{1}{2}\{ {( {v_{gd} + \delta} )\sqrt{( {v_{gd} + \delta} )^{2} + {4\delta}}} \}\mspace{121mu} 21.2b\mspace{14mu}\frac{Q_{{overlap},d}}{W_{diodCV}}} = {{{{CGD}\;{0 \cdot V_{gd}}} + {{CGD}\; 1\{ {V_{gd} - V_{gd\_ overlap} + {\frac{CKAPPA}{2}( {{- 1} + \sqrt{1 + \frac{4V_{gd\_ overlap}}{CKAPPA}}} )}} \} 21.3\mspace{14mu}{Gate}\mspace{14mu}{Overlap}\mspace{14mu}{Charge}{21.3.a}\mspace{14mu} Q_{{overlap},g}}} = {{{{- ( {Q_{{overlap},s} + Q_{{overlap},d}} )}21.4\mspace{14mu}{Source}\text{/}{Drain}\mspace{14mu}{Junction}\mspace{14mu}{Charge}{For}\mspace{14mu} V_{bs}} < {0.95\phi_{s}{21.4.a}{.1}\mspace{14mu} Q_{jswg}}} = {{Q_{bsdep} + {Q_{bsdif}{else}{21.4.a}{.2}\mspace{14mu} Q_{jswg}}} = {C_{bsdep}( {{{{0.95{\phi_{s}( {V_{bs} - {0.95\phi_{s}}} )}} + {Q_{bsdif}{For}\mspace{14mu} V_{bd}}} < {0.95\phi_{s}{21.4.a}{.3}\mspace{14mu} Q_{jdwg}}} = {{Q_{bddep} + {Q_{bddif}{else}{21.4.a}{.4}\mspace{14mu} Q_{jdwg}}} = {{{{C_{bddep}( {0.95\phi_{s}} )}( {V_{bd} - {0.95\phi_{s}}} )} + {Q_{bddif}{where}{21.4.b}{.1}\mspace{14mu} Q_{bsdep}}} = {{W_{diosCV}C_{jswg}\frac{T_{si}}{10^{- 7}}{\frac{P_{bswg}}{1 - {Mj}_{swg}}\lbrack {1 - ( {1 - \frac{V_{bs}}{P_{bswg}}} )^{1 - M_{jswg}}} \rbrack}{21.4.b}{.2}\mspace{14mu} Q_{bddep}} = {{W_{diodCV}C_{jswg}\frac{T_{si}}{10^{- 7}}{\frac{P_{bswg}}{1 - {Mj}_{swg}}\lbrack {1 - ( {1 - \frac{V_{bd}}{P_{bswg}}} )^{1 - M_{jswg}}} \rbrack}{21.4.b}{.3}\mspace{14mu} Q_{bsdif}} = {{\frac{W_{eff}^{\prime}}{N_{seg}}T_{si}{{J_{sbjt}\lbrack {1 + {L_{{dif}\; 0}( {L_{{bj}\; 0}( {\frac{1}{L_{eff}} + \frac{1}{L_{n}}} )}^{N_{dif}} )}} \rbrack}\lbrack {{\exp( \frac{V_{bs}}{n_{dio}V_{t}} )} - 1} \rbrack}\frac{1}{\sqrt{E_{blis} + 1}}{21.4.b}{.4}\mspace{14mu} Q_{bddif}} = {{\frac{W_{eff}^{\prime}}{N_{seg}}T_{si}{{J_{sbjt}\lbrack {1 + {L_{{dif}\; 0}( {L_{{bj}\; 0}( {\frac{1}{L_{eff}} + \frac{1}{L_{n}}} )}^{N_{dif}} )}} \rbrack}\lbrack {{\exp( \frac{V_{bd}}{n_{dio}V_{t}} )} - 1} \rbrack}\frac{1}{\sqrt{E_{blid} + 1}}{21.4.b}{.5}\mspace{14mu} C_{jswg}} = {{{C_{{jswg}\; 0}\lbrack {1 + {t_{cjswg}( {T - T_{nom}} )}} \rbrack}{21.4.b}{.6}\mspace{14mu} P_{bswg}} = {{P_{{bswg}\; 0} - {{t_{pbswg}( {T - T_{nom}} )}22\mspace{14mu}{Extrinsic}\mspace{14mu}{Capacitance}22.1\mspace{14mu}{Bottom}\mspace{14mu} S\text{/}D\mspace{14mu}{to}\mspace{14mu}{Substrate}\mspace{14mu}{Capacitance}\mspace{104mu} C_{{sld},e}}} = \{ {{\begin{matrix}C_{box} & {if} & {V_{{sld},e} < V_{sdfb}} \\{C_{box} - {\frac{1}{A}( {C_{box} - C_{\min}} )( \frac{V_{{sld},e} - V_{sdfb}}{V_{sdth} - V_{sdfb}} )^{2}}} & {elseif} & {V_{{sld},e} < {V_{sdfb} + {A_{sd}( {V_{sdth} - V_{sdfb}} )}}} \\{C_{\min} + {\frac{1}{1 - A_{sd}}( {C_{box} - C_{\min}} )( \frac{V_{{sld},e} - V_{sdfb}}{V_{sdth} - V_{sdfb}} )^{2}}} & {elseif} & {V_{{sld},e} < V_{sdth}} \\C_{\min} & {else} & \;\end{matrix}22.2\mspace{14mu}{Sidewall}\mspace{14mu} S\text{/}D\mspace{14mu}{to}\mspace{14mu}{Substrate}\mspace{14mu}{Capacitance}C_{{sld},{esw}}} = {C_{sdesw}{\log( {1 + \frac{T_{si}}{T_{box}}} )}}} }}}}}}}}} }}}}}}}}} }} }} }} }}}}}}} }}} }}}}}}} }$

1. A computer-implemented method for modeling devices having differentgeometries in an integrated circuit using a device model, comprising:dividing a geometrical space including the different geometries into afirst set of subregions and a second set of subregions, the first or thesecond set of subregions including one or more subregions, wherein eachof the second set of subregions includes at least some portion that isnot included in the first set of subregions; extracting a set of modelparameters for each of the first set of subregions using model equationsassociated with the device model and measurement data obtained from aplurality of test devices; determining binning parameters for each ofthe second set of subregions using one or more model parametersassociated with one or more subregions in the first set of subregions;and saving at least some of the model parameters or the binningparameters in one or more files.
 2. The method of claim 1, wherein eachof the first set of subregions is bordered by one of the second set ofsubregions.
 3. The method of claim 1, wherein each of the first orsecond set of subregions covers a subrange of device geometry variationswithin the geometrical space.
 4. The method of claim 1, wherein themeasurement data include measured values of a set of physical quantitiesassociated with the test devices and extracting a set of modelparameters for each of the first set of subregions comprises:calculating values of the set of physical quantities associated with thedevices using model equations and an initial guess of the values of theset of model parameters; and adjusting the values of the set of modelparameters by fitting the calculated values of the set of physicalquantities with the measurement data.
 5. The method of claim 1, whereinthe measurement data used to extract model parameters for a subregioninclude current and capacitance data measured from the plurality of testdevices.
 6. The method of claim 5, wherein the plurality of test devicesinclude test devices whose geometries are within or on borders of thesubregion.
 7. The method of claim 1, wherein determining binningparameters for each of the second set of subregions comprises: selectinga model parameter for binning; determining boundary values of theselected model parameter; and solving for the binning parametersassociated with the selected model parameter using the boundary values.8. The method of claim 7, wherein the boundary values of the selectedmodel parameter are determined based on one or more extracted parametersin one or more subregions in the first set of subregions.
 9. The methodof claim 8, wherein the one or more subregions in the first set ofsubregions are adjacent the subregion for which binning parameters aredetermined.
 10. The method of claim 7, wherein solving for the one ormore binning parameters comprises expressing the selected modelparameter as a function of device geometry instances in the subregion,the function including the one or more binning parameters associatedwith the selected model parameter as coefficients.
 11. A computerreadable storage medium comprising computer executable programinstructions that when executed cause a digital processing system toperform a method for modeling devices having different geometries in anintegrated circuit, the method comprising: dividing a geometrical spaceincluding the different geometries into a first set of subregions and asecond set of subregions, the first or the second set of subregionsincluding one or more subregions, wherein each of the second set ofsubregions includes at least some portion that is not included in thefirst set of subregions; extracting a set of model parameters for eachof the first set of subregions using model equations associated with adevice model and measurement data obtained from a plurality of testdevices; determining binning parameters for each of the second set ofsubregions using one or more model parameters associated with one ormore subregions in the first set of subregions; and saving at least someof the model parameters or the binning parameters in one or more files.12. The computer readable storage medium of claim 11, wherein each ofthe first set of subregions is bordered by one of the second set ofsubregions.
 13. The computer readable storage medium of claim 11,wherein each of the first or second set of subregions covers a subrangeof device geometry variations within the geometrical space.
 14. Thecomputer readable storage medium of claim 11, wherein the measurementdata include measured values of a set of physical quantities associatedwith the test devices and extracting a set of model parameters for eachof the first set of subregions comprises: calculating values of the setof physical quantities associated with the devids using model equationsand an initial guess of the values of the set of model parameters; andadjusting the values of the set of model parameters by fitting thecalculated values of the set of physical quantities with the measurementdata.
 15. The computer readable storage medium of claim 11, wherein themeasurement data used to extract model parameters for a subregioninclude current and capacitance data measured from the plurality of testdevices.
 16. The computer readable storage medium of claim 15, whereinthe plurality of test devices include test devices whose geometries arewithin or on borders of the subregion.
 17. The computer readable storagemedium of claim 11, wherein determining binning parameters for each ofthe second set of subregions comprises: selecting a model parameter forbinning; determining boundary values of the selected model parameter;and solving for the binning parameters associated with the selectedmodel parameter using the boundary values.
 18. The computer readablestorage medium of claim 17, wherein the boundary values of the selectedmodel parameter are determined based on one or more extracted parametersin one or more subregions in the first set of subregions.
 19. Thecomputer readable storage medium of claim 18, wherein the one or moresubregions in the first set of subregions are adjacent the subregion forwhich binning parameters are determined.
 20. The computer readablestorage medium of claim 17, wherein solving for the one or more binningparameters compnses expressing the selected model parameter as afunction of device geometry instances in the subregion, the functionincluding the one or more binning parameters associated with theselected model parameter as coefficients.
 21. A digital processingsystem for modeling devices having different geometries in an integratedcircuit, comprising: a central processing unit (CPU); a memory devicecoupled to the central processing unit and storing therein computerexecutable program instructions that when executed by the CPU cause thedigital processing system to perform a method for modeling deviceshaving different geometries in an integrated circuit, the methodcomprising: dividing a geometrical space including different geometriesinto a first set of subregions and a second set of subregions, the firstor the second set of subregions including one or more subregions,wherein each of the second set of subregions includes at least someportion that is not included in the first set of subregions; extractinga set of model parameters for each of the first set of subregions usingmodel equations associated with a device model and measurement dataobtained from a plurality of test devices; determining binningparameters for each of the second set of subregions using one or moremodel parameters associated with one or more subregions in the first setof subregions; and saving at least some of the model parameters or thebinning parameters in one or more files.
 22. The digital processingsystem of claim 21, further comprising an input port for inputting themeasurement data from the plurality of test devices.